If gender is innate, if girls and boys are just naturally different and naturally like different things, want different things, show different behaviors, why do we have to put so much effort, so much work into separating them?

If gender was innate it wouldn't have to be indoctrinated into anyone. Everyone would naturally pick what they want to pick, and every girl would pick the same thing while every boy would pick the opposite. We would never have to tell any little girl or little boy anywhere, “this is not for you, it’s for boys/girls”.