But genes affect cognition and behavior, so you've got a false dichotomy looming.

Furthermore, though you state, "What made our behavior work is our ability to express a broad spectrum of gender.", I can provide plenty of counterexamples throughout history, where gender roles were narrowly construed and people reproduced just fine--can't you?

So I think you're leaning a too much on evolution here. Firstly, cultural "evolution" isn't technically evolution because it isn't "descent with modification" but involves a crazy amount of mixing and blending of cultures these days. Secondly, the biggest damper on reproduction in recent decades is economic development (which is, for now, a good thing because we're way over carrying capacity for the world's population to have the level of development of the world's most economically prosperous countries). Modern-day facilitation of a broad spectrum of gender roles tends to be positively correlated with economic development, so the sign is backwards at the moment.

But it doesn't matter.

Evolution is slow. Culture is fast. We're in a cultural shift now; evolution can catch up later.