Unless he's changed his tune in the last two or three weeks, he's been very cagey about relating his work on linguistics to politics, and the definition of "human nature" is kept off in the realm of conjecture. In one _vuelta_ on Znet, he escaped into common sense -- it's our _nature_ to have four arms instead of two, etc., so of course there is _some_ kind of stable human nature, and so on. Even so, some anarchists have decided, on the basis of such weak passes at delineating "human nature" as this, that he's some sort of fascist who knows what's good for everybody. You can't win.
As for "postmodernism", everyone's fond of Chomsky's denunciations of it, since he says he doesn't read the stuff. This seems to be a prerequisite, so he's a credentialled anti-postmodernist.
Gordon