Its a complex thing here.
Even if gender is innate, I see more as a guideline, and map for learning.
That explain the vast disparity in behavior and expression even in people brought up just about the same.
Meaning, you absorb information differently, use it differently, than a male, because of this born predisposition.
But, what information you are expose to, still has a big influence since you cannot work from nothing.
Also, there is a couple of thing here.
There is unconscious or environmental directed learning (the only on in very young children) , directed learning (somewhat exposes you to specific information) and self-directed learning (you are the one seeking the information according to inner predisposition and prior learning).
So, if someone dresses you in pink clothes and surrounds you with dolls since you were born, what do you take from this? If someone takes your a girl and your dad puts you on the hockey team at 5, or takes you hunting at 8, or builds robots with you from age 4, what influences does this have? Do you then become a star female hockey player, reading everything you can about bodychecking, or collect guns, read guns and ammo, and become a swat team sharpshooter. Or, maybe go to MIT in engineerig and build a robot called Robbie soon to lost in space...
I think, we like to simplify things. Because it would be simpler if the reason why women and men are different and where does this difference comes from was clear cut.
As we see with gender variants, and androgynes and the huge variance in TS's and women's gender expression, it cannot be that simple, because there is to much variance to be explained by something simple.