"To the pure, all things are pure, but to the defiled and unbelieving, nothing is pure; but both their minds and their consciences are defiled. They profess to know God, but they deny him by their works. They are detestable, disobedient, unfit for any good work." - Titus 1:15-16
First of all I would like to say that Paul writes similar language in which he writes in Romans 14 and perhaps elsewhere. The kingdom of God is not about eating or drinking, but about righteousness and peace and joy in the Holy Spirit. To the pure all things are pure. Nothing can separate you dear Christian who have now received Christ as Saviour from the love of God. There is no clean thing to abstain from.
However, second, for the unbelieving one nothing is pure. All things are unclean to him. While they may take the things that God created as good and distort them for their own evil purposes and intentions ultimately they are damnable to God.
Thirdly, about these men although they may profess to know God as in the Gospel, they in fact deny him by their works. Please read this carefully. This means not that they sinned necessarily did things against God's holy character or nature - although that may be true. However, it is just as much true that they as the Jews did in Romans 10 that although they have a zeal for God, but not according to knowledge. Scripture says that Christ is the end of the law for all who believe. What this text tells us is that salvation is by grace alone and not by works. No man can boast before God's sovereign grace. However, these men in their pride self-righteousness - perhaps circumcising themselves (Judiazers) - denied the God, who saves us in Christ alone by grace alone through faith alone, by their works. (I hope this is clear please if you have any questions ask)