This quotation taken from Epimenides and utilised by the Apostle Paul is used by some to argue that Paul was 'taking on' the evil forces at work in the culture. He was challenging the culture of Crete and therefore those Christians who argue for Two Kingdom theology, those Christians who reject Dominionism are necessarily in error.
Actually this verse is but another example of Paul 'not' taking on society, very much like Peter in his first epistle arguing that as strangers and pilgrims they were to have their conduct honourable among the Gentiles... by obeying the government and submitting to suffering. Peter didn't even bother to address slavery per se.
Of course some Dominionists use this final point as justification for their own historical narratives, but that's another topic.
Paul acknowledges there are problems in the culture of Crete. Titus is not to address the Cretans outside the confines of the Church/Kingdom. They would be unable to understand or respond to the call of sanctification or the demands of mortification and renewal. For those 'outside' there is little more to do with them apart from leading them to the Gospel. 1Cor 5.9-13 and Romans 8.5-8 emphasize this same point of antithesis between the Church and the world and the futility of trying to impose Christian morality on lost and unconverted people.
If we can convince people that sin condemns them and if they come to understand that therefore their culture is sinful, then all is well and good but that's only possible under the power and guidance of the Holy Spirit. The call to repentance in condemning sin is a means the Holy Spirit uses to convict but the real problem of the Cretans (or Americans) is not their gluttony or lies but their rejection of Christ as Messiah.
But when they become Christians then their lying and gluttony can be understood and addressed. They have a new authority, one that the Holy Spirit makes effectual in their lives, one they can (in the Spirit) submit to.
Titus is not to address the culture. He's addressing the Church.
You will often hear people who argue in this fashion assert that Two Kingdom missionaries won't address the problems of a culture. This is completely false. The difference is they don't look to convert the chieftain or ruler and then encourage him to mandate the change through legislation. That's the medievalist and Sacralist model that creates a type of cultural Christianity and 'converts' it into a civil religion. It creates an outward conformity and veneer but does nothing in terms of the heart. Civil laws (rules backed by threat) cannot generate saving faith.
The missionaries address their converts and the sinful behaviour they bring with them into the Church. It creates difficulties as all mission work does. There are ways to deal with. It's interesting that on the American frontier it was the Moravian missionaries who were most effective in gaining converts and living at peace with Indians. In some cases it meant creating Christian villages. Living alongside their pagan brethren was too difficult but the Moravians weren't going to demand the Indians become Europeans either. There was a way to apply Christianity in their context. They weren't always appreciated by the colonial governors but they were highly respected by the Indians. They weren't viewed as conquerors even though to some degree they were derailing the Native American order of things. Later after the French and Indian War and the American Revolution the only white Europeans, the only Christians the Indians would respect were the Moravians and the Quakers.
They followed Paul's injunctions. The Transformationalists who use this verse from the Epistle to Titus twist its meaning and distort its context in order to justify their lusts for power and the theology they have created in order to rationalise it.
The Church at present would be better served by purging American culture and its sinful proclivities from its own ranks rather than waging the Culture War which only confuses the Gospel and makes its offense not rooted in the Person and Work of Christ but a result of social threat and intimidation.