The answer is 'not much, really', I guess. To the extent that it had an influence, it was only because it was really easy to stick elements of it into discourses that were already extremely fashionable.
Oddly enough for a thread which touches on evolution and society, I find myself pretty much agreeing with Al here. One can argue whether any particular question is or is not a scientific question. For example, I'd see "what is human nature?" as a scientific question, while many others on this forum would not. When it comes to using science (or not using science, or opposing the use of science) to answer philosophical questions, however, it's essentially a tool that can be used whichever way the debater wishes. Witness, for example, the fact that my political views fall much closer to the people on this thread who have in the past hated on evolutionary psychology than those who haven't