If everyone starts from the same place it's fine to say "give everyone equal opportunity". If you really want to have equal opportunity given the historical and social background you have to acknowledge that everyone doesn't start from the same place.
And how exactly does it translate to gender? If anything, I would argue that most women have much better background. Not that it matters anyway. If an immigrant from 3rd world country can come to US at age 30 and be better than the competition, then you pretty much have no excuse if you were born here.
I suspect that they would not be if there would be an equal opportunity. Not giving people a chance just because of ideology is despicable. That's my point.
If people truly want equality, it shouldnt even be a factor. No prejudice. Just treat all as of us one thing, human being.