This section, the last section in chapter 1, has 4 verses.

To set the stage, let us read the previous four verses.

Titus 1:9-12
9 Holding fast the faithful word as he hath been taught, that he may be able by sound doctrine both to exhort and to convince the gainsayers.
10 For there are many unruly and vain talkers and deceivers, specially they of the circumcision:
11 Whose mouths must be stopped, who subvert whole houses, teaching things which they ought not, for filthy lucre's sake.
12 One of themselves, even a prophet of their own, said, The Cretians are alway liars, evil beasts, slow bellies.

Now to the last four verses of the chapter

Titus 1:13-16
13 This witness is true. Wherefore rebuke them sharply, that they may be sound in the faith;
14 Not giving heed to Jewish fables, and commandments of men, that turn from the truth.
15 Unto the pure all things are pure: but unto them that are defiled and unbelieving is nothing pure; but even their mind and conscience is defiled.
16 They profess that they know God; but in works they deny him, being abominable, and disobedient, and unto every good work reprobate.

We will begin with the Barclay. This commentary covering all four verses [13-16].  The first three sentences are verses 13-16 paraphrased.

THE PURE IN HEART
For that very reason correct them with severity, that they may grow healthy in the faith and not pay attention to Jewish fables and to rules and regulations made by men who persist in turning their backs on the truth.

‘To the pure, all things are pure.’

But, to those who are defiled and who do not believe, nothing is pure, because their mind and conscience are defiled. They profess to know God, but they deny their profession by their deeds, because they are repulsive and disobedient and useless for any good work.

THE great characteristic of the Jewish faith was its thousands of rules and regulations. Many things were branded as unclean; many kinds of food were classified as forbidden. When Judaism and Gnosticism joined hands, even the body became unclean, and the natural instincts of the body were held to be evil. The inevitable result was that long lists of sins were constantly being created. It became a sin to touch certain things; it became a sin to eat certain foods; it even became a sin to marry and to have children. Things which were either good in themselves or quite natural were considered unclean.

It is the heart which makes all the difference. If someone is pure in heart, all things are pure to that person. If someone is unclean in heart, then everything that person thinks about or speaks about or touches becomes unclean. This was a principle which the great classical writers had often stated. ‘Unless the vessel is pure,’ said Horace, ‘everything you pour into it grows bitter.’ Seneca said: ‘Just as a diseased stomach alters the food which it receives, so the darkened mind turns everything you commit to it to its own burden and ruin. Nothing can come to evil men which is of any good to them, nay nothing can come to them which does not actually harm them. They change whatever touches them into their own nature. And even things which would be of profit to others become pernicious [harmful] to them.’ The person with a dirty mind makes everything dirty, taking even the loveliest things and covering them with smut. But the person whose mind is pure finds purity in everything.

It is said of these people that both their minds and their consciences are contaminated. We come to decisions and form conclusions by using two faculties. We use intellect to think things out; we use conscience to listen to the voice of God. But if the intellect is warped in such a way that it sees the unclean everywhere and in all things, and if the conscience is darkened and numbed by continual consent to what is evil, it becomes impossible to take any good decision at all.

If we allow impurity to infect the mind, we will see all things through a mist of uncleanness. The infected mind soils every thought that enters into it; the imagination turns every picture which it forms into a source of lust. Every motive is misinterpreted. Every statement is given a double meaning. To escape that uncleanness, we must walk in the cleansing presence of Jesus Christ.

THE UGLY AND THE USELESS LIFE
WHEN people get into this state of impurity, they may know God intellectually but their lives are a denial of that knowledge. Three things are singled out here about such people.

(1) They are repulsive. The word (bdeluktos) is the word particularly used of idols and images. It is the word from which the noun bdelugma, an abomination, comes. There is something repulsive about someone with an obscene mind, who makes sniggering jokes and whose comments are full of innuendo.

(2) They are disobedient. Such people cannot obey the will of God. Their consciences are darkened. They have made it almost impossible for themselves to hear the voice of God, let alone obey it. People like that cannot be anything but an evil influence and are therefore unfit to be instruments in the hand of God.

(3) That is just another way of saying that they have become useless to God and to others. The word used for useless (adokimos) is interesting. It is used to describe a counterfeit coin which is below standard weight. It is used to describe a cowardly soldier who fails in the testing hour of battle. It is used of a candidate rejected for public office, someone whom the citizens regarded as useless. It is used of a stone which the builders rejected. (If a stone had a flaw in it, it was marked with a capital A, for adokimos, and left to one side, as being unfit to have any place in the building.) The ultimate test of life is usefulness, and those who are a bad influence and who have a contaminating effect are of no use to God or to other people. Instead of helping God’s work in the world, they hinder it; and uselessness always invites disaster. ~Barclay Commentary

Now to the other commentaries. We will begin with the general commentaries and spend this whole less there.

This from the Matthew Henry Main where I am breaking in to a long commentary covering verses 6-16.

6. He gives the reasons of this, from the liberty we have by the gospel from legal observances, and the evil and mischief of a Jewish spirit under the Christian dispensation in the last two verses. To good Christians that are sound in the faith and thereby purified all things are pure. Meats and drinks, and such things as were forbidden under the law (the observances of which some still maintain), in these there is now no such distinction, all are pure (lawful and free in their use), but to those that are defiled and unbelieving nothing is pure; things lawful and good they abuse and turn to sin; they suck poison out of that from which others draw sweetness; their mind and conscience, those leading faculties, being defiled, a taint is communicated to all they do. The sacrifice of the wicked is an abomination to the Lord, Proverbs 15:8. And Proverbs 21:4, The ploughing of the wicked is sin, not in itself, but as done by him; the carnality of the mind and heart mars all the labour of the hand. ~Matthew Henry Main

Note: I want to make a clear distinction here.  The things that are pure are all the things that are lawful before God. What is being referred to here are the massive amount of added law by the Jews of the time.  We are absolutely not speaking to clean and unclean meats here.  Unclean meats remain unclean for all time.

Now to the Matthew Henry Concise which covers verses 10-16,

False teachers are described. Faithful ministers must oppose such in good time, that their folly being made manifest, they may go no further. They had a base end in what they did; serving a worldly interest under pretence of religion: for the love of money is the root of all evil. Such should be resisted, and put to shame, by sound doctrine from the Scriptures. Shameful actions, the reproach of heathens, should be far from Christians; falsehood and lying, envious craft and cruelty, brutal and sensual practices, and idleness and sloth, are sins condemned even by the light of nature. But Christian meekness is as far from cowardly passing over sin and error, as from anger and impatience. And though there may be national differences of character, yet the heart of man in every age and place is deceitful and desperately wicked. But the sharpest reproofs must aim at the good of the reproved; and soundness in the faith is most desirable and necessary. To those who are defiled and unbelieving, nothing is pure; they abuse, and turn things lawful and good into sin. Many profess to know God, yet in their lives deny and reject him. See the miserable state of hypocrites, such as have a form of godliness, but are without the power; yet let us not be so ready to fix this charge on others, as careful that it does not apply to ourselves. ~Matthew Henry Concise

Now a couple of items from the Biblical Illustrator.  This subject of purity can be a complex one and its explanation in the Biblical Illustrator can be abundantly wordy.  You are not going to get absolute clarity with my reading of it.  You will have to slowly read and reread this and do some meditation and even some praying.

Purity
I. Who are meant by pure persons. The persons here called pure are such as by faith are set into Christ [are firstfruits], by whose blood they are justified, and by whose Spirit, through the means of the Word, that immortal seed of regeneration, they are sanctified and reserved unto life everlasting. And hence to both these is the purifying and cleansing of sinners ascribed in the Scriptures.

1. Because by faith every member of the Church layeth hold upon Christ’s most absolute purity.
2. The spirit of regeneration hath washed every part, although in part only, nor so clean as it shall be, yet so as that perfect purity is sealed and assured to the soul by it.
3. The Lord doth account every such believer pure even for the present, and imputeth never a spot unto them, but reputeth in His Christ all fair.
4. Hath promised them that for time to come they shall become so absolutely clean as though they had never been defiled.

II. How all things are pure or impure.
1. Seeing all things were pure in their creation, we may herein, as in a glass, behold the purity of God in all His creatures, admiring that goodness of His which bewrayed [shows] itself even in the meanest of them; yea, provoking ourselves to love, reverence and fear before Him, the image of whose goodness shineth out not only in angels and men, but even in the silly worm and fly, yea in the lifeless creatures themselves. And further, hence we may gather our own duty towards the creatures, namely

(1) Reverently meditate and speak of them.
(2) Purely to use them.
(3) Mercifully to deal with them. All which we shall the easier do if we can spy out some part of God’s image in them.

2. The restitution of us to our former right is only from our Lord Jesus Christ, and our first right is recovered to us in this manner. First, as we were at odds with the Creator, and consequently with the creature, even so first we are reconciled unto God through Christ, and then to the creatures; for when Christ (who is our peace) hath wrought our peace with God, He bringeth back our peace, both the inward peace of our own consciences, which before could do nothing but accuse and terrify, as also peace with others, friends and enemies, yea even with the beast of the field, and stone in the wall, and everything striketh a covenant of peace with him who hath entered into league with the Creator of it. If any man, then, would have any right in any creature he useth, he must not hold it by the broken title in the first Adam, but by a recovered and new purchase in the second Adam, who is the Lord of glory, blessed forever.

III. How all things are pure to the pure. That we may rightly and properly conceive the apostle’s meaning, we must know
1. That the universal particle “all things” admitteth restraint, and may not be extended beyond the apostle’s intendment, who speaketh only of such things as are not forbidden by the law of God, or nature; or rather only of things of an indifferent nature, which in themselves are neither commanded nor forbidden, and neither good nor evil in their substance and nature, but are to be used or not used according to the circumstances and occasions of them; such things as these are meat, drink, apparel, recreation, sleep, marriage, single life, riches, poverty, bondage, freedom, etc. And it may not seem strange thus to restrain this general proposition, seeing we have it thus limited in sundry other places (1 Corinthians 6:4). “All things are lawful, but not profitable” (1 Corinthians 10:23). “All things are lawful for me, but not expedient” (Romans 14:20). “All things indeed ere pure, but destroy not for meats,” etc.

Quoted verses:
1 Corinthians 6:4
If then ye have judgments of things pertaining to this life, set them to judge who are least esteemed in the church.

1 Corinthians 10:23
All things are lawful for me, but all things are not expedient: all things are lawful for me, but all things edify not.

Romans 14:20
For meat destroy not the work of God. All things indeed are pure; but it is evil for that man who eateth with offence.

2. By pure is meant nothing else but that all such things are free now to be used in good conscience, without scruple, by means of our Christian liberty.
3. In that he addeth “to the pure,” he showeth how we come to have title in this liberty, even by becoming believers and getting our hearts purified by faith. In one word, all indifferent things are pure, and free to be used of the pure and believing person, with this one condition; so they be purely and rightly [lawfully] used.

Purity of mind indispensable
I. The import of the terms. By “the pure” is not meant sinless. Evangelical purity is connected with faith (1 Peter 1:22; Acts 15:9). The mind and conscience are governing powers; if they be polluted, all the man is so.

Quoted verses:
1 Peter 1:22
Seeing ye have purified your souls in obeying the truth through the Spirit unto unfeigned love of the brethren, see that ye love one another with a pure heart fervently:

Acts 15:9
And put no difference between us and them, purifying their hearts by faith.

Note: The "us and them" here are the Jews and Gentiles; the circumcised and uncircumcised.

II. Illustrate the sentiment.
1. On a believing mind the doctrines of Christ will have a sanctifying effect, and the contrary on an unbelieving mind.
2. On a believing mind precepts and even threatenings produce a salutary effect.
3. Mercies and judgments humble, melt, and soften some, but harden others.
4. The evils which occur amongst men, differently influence different characters.
5. The treatment received from men brings out the state of the heart.

Even their mind and conscience is defiled
The faithlessness of conscience

Note:  The text below is speaking about the defiled mind.

That the conscience is so perverted in our present condition, that no confidence can be placed in its decision, is evident.
I. From the fact that these decisions can be correct in no other cases but those in which Divine truth is fully understood.
II. That the decisions of conscience are not always in accordance with the truth is evident from the fact that sinners are not always convinced of sin.
III. This position is also sustained by the fact that the agency of the Holy Spirit is requisite to convince the world of sin.
IV. The faithlessness of conscience is apparent in the fact that hypocrites have not always an appalling sense of their hypocrisy.

V. This view of the subject is strengthened by the fact that even Christians do not always detect their own sins.
VI. This doctrine is evident from the fact that there is no command in the Scriptures to follow the dictates of conscience.
VII. And while there is no direction to follow the dictates of conscience, it is true that the Scriptures designate different consciences, and perhaps different states of the same conscience, by different and directly opposite terms.
VIII. This view of the subject is confirmed by the fact that the way to ruin seems to be the way of peace and eternal life. This is a very common and perhaps a general trait of the human family. The light that is in them by nature is darkness. They discern not the way in which they should go.  

RECAP
Besides the false doctrines and false teachers that abound then and now, certain men, such as the Pharisees and Scribes had added all kinds of laws to the true Christian faith.
As we saw in verse 14, these Jewish fables and commandments of men had the power to turn us from the truth.
These individuals who create these commandments of men have turned their backs on the truth.

Three things we know about these individuals:
1] They are repulsive.
2] They are disobedient.
3] They are useless to God and others.

To the faithful firstfruit, all things are pure. That is, all things God made are good and have their place in the world.
Firstfruits do all things on earth lawfully.
Firstfruits let God and His Word direct their lives
The vain talkers and deceivers do not heed God.

Shameful actions and the reproach of heathens should be far from Christians.
Firstfruits should not be too ready to judge hypocrites so much as they be focused on the self to make sure we gather no traits of the hypocrites.

We are in a process created by God to the purifying and cleansing of sinners ascribed in the Scriptures.
Firstfruits spend their lives laying hold of the purity of Christ.

God made all things on the earth in purity. In nature, we can see God in every animal, plant and rock that He made.

The phrase, "all things are pure" comes with restraint meaning that we can use all things and do all things only in accordance with law and the Word of God.

All things are pure, and free to be used of the pure and believing person, with this one condition; so they be purely and rightly [lawfully] used.

Evangelical purity is connected with faith [1 Peter 1:22].

The doctrines of God have a sanctifying effect on the firstfruit mind.

Not all hypocrites know that they are hypocrites.

There is nothing in scripture commanding us to follow the dictates of conscience. We are to follow the dictates of God. The power of God works with your conscience to do all things lawfully.

These are the lessons of verse 15.