Not wanting to appear rude, but do any of you actually know what post-modernism IS? Have you ever read any? Or are you just going by what you've heard?
It's perfectly compatible with scepticism, and indeed can be a tool of a sceptical approach. Post-modern approaches to gender, race and sexuality have informed liberalism for most of the second half of this century. Believe me, you all engage in post-modern thought whether you'd care to admit it or not. The type of thought and communication the internet has facilitated is extremely post-modern, as are the founding principles of things like Open Source Software and Wikipedia.
It's true that post-modernism has had its embarrassments - the Sokal affair being maybe the most well known - but considering a comparable occurrence concerning the Journal of Reproductive Medicine recently, I don't think that's reason enough to throw the baby out with the bathwater.
Postmodernism, despite Dawkin's mischaracterisation, does not posit "everything is true", despite what you've heard.