The view you essentially describe is indeed held by some Christians, but this is not postmodernism.
Postmodernism implies a denial of absolute truth, and I assume that your question arises because if many Christians deny an absolute definition of modesty, this seems to imply, to some degree, a denial of absolute truth.
But that is not the case. Denying an absolute modesty dress code does not imply the denial of an absolute principle of modesty. In other words, the Christians you describe still hold themselves to an absolute truth - but that truth is a principle of modesty, and not a legalistic dress code. The Bible does cover the principle of modesty, though what that looks like in practice will vary greatly from culture to culture, and from conscience to conscience.
This principle of modesty is described much better by C.S. Lewis in Mere Christianity (emphasis added):
The Christian rule of chastity must not be confused with the social rule of 'modesty' (in one sense of that word); i.e. propriety, or decency. The social rule of propriety lays down how much of the human body should be displayed and what subjects can be referred to, and in what words, according to the customs of a given social circle. Thus, while the rule of chastity is the same for all Christians at all times, the rule of propriety changes. A girl in the Pacific islands wearing hardly any clothes and a Victorian lady completely covered in clothes might both be equally 'modest', proper, or decent, according to the standards of their own societies: and both, for all we could tell by their dress, might be equally chaste (or equally unchaste).
 See Romans 14
 Note that C.S. Lewis distinguishes between "modesty" and "chastity", and uses the word "modesty" only to describe social propriety. In my answer, I have used the phrase "principle of modesty" in the same way he uses the word "chastity"