Politics and evo psych
Thanks to Smerdis' recent rants I've been reading up on the nature of feminist/postmodernist objections to EP (regarding what behaviours are generated by the mind via biology/genetics compared to culture). Regardless of the falsifiability issues of EP, what studies do the left-wing side specifically object to?
I don't pay much attention to the postmodernists. Some of the leftist criticism of EP is a spillover of the sociobiology wars coming from scientist-activists like Lewontin and co. Far more interesting and substantive critiques are coming from within EP itself or related fields. Is there anything specific you're looking for?
Gender, specifically. Is there any significant study (ie. not pop psychology) that conflicts with the mainstream goals of gender equality? EP is likely the scientific field that I'm least familiar with.
I highly doubt there is anything in the technical literature that, by itself, conflicts with said goals. However, there is a good bit of research that is based on assumptions of '50s-style gender roles. The most notorious is, probably, the work on mating preference and parental investment. The cornerstone of this research program is David Buss' 1989 cross-cultural study. His interpretation of the results have been heavily criticized (e.g., Eagly and Wood and Buller.).