(Reposted from the previous OT)

One of my professors claimed that postmodernism, and particularly its concept of "no objective truth", is responsible for much of the recent liberalism of society, through the idea of "live and let live". (Specific examples given were attitudes towards legalization of gay marriage and drugs.) I pointed out that libertarianism and liberalism predated postmodernism historically, and they said that that's true, but you can still trace the popularity back to postmodernism.

Is this historically accurate? If not, is there something I can point to that would convince them? It seems to me that the shift in society is much more a shift on the object level questions than on the meta level "should we ban things we disagree with", but I don't know very much recent history of philosophy (it isn't strictly their field either, so I'm justified in not taking them at face value).