Gender differences definitely do exist - the question to prove is if they are small or orthogonal to actual ability, or somehow relevant. For example, if a job position requires hauling refrigerators to customers, then the requirements do favor males, and a genetic subset of them with large body frames. The question is, if any of this actually applies to positions such as orchestra musician or mathematician?

There are many studies about significant differences between twins caused by a single gene expression. There are studies about differences in physical properties, mental abilities and inherited diseases linked to genes of ethnic/racial groups - I believe the Ashkenazi case is the most popular, but there are others. And there are numerous studies about male/female differences - for example, in expressiveness of agression, average temperament and different cooperate/defect-style decisions in game theory and econometrics experiments.

But it all is irrelevant - the whole concept of gender/race/etc equality is that it is grossly unfair to use group-membership to judge individuals, and we should evaluate each person on her/his own merits.