I havent dove into evidence much during this discussion, but I agree that it is a good place to argue from. (I would tend to echo a good few Jordan Peterson-style points, such as gender employment ratios in scandinavian egalitarian countries, differences by gender in OCEAN personality factors, etc). I do think there is substantial evidence that personality trait differences between women and men correlate highly across the globe. This should add up to substantial (although not conclusive) evidence that preferences would also be different between genders. Conclusive evidence is impossible without having some hypothetical cultureless test case. I also believe that social science as practiced today is poorly equipped to conclusively answer these questions. Any individual must therefore decide for themselves what their predictions would be on a number of gender-related issues.

"Given an unbiased society, would I expect an equal number of male and female bricklayers?" I would not.

"Given an unbiased society, would I expect an equal number of male and female biologists?" I would not.

"Nurses?" I would not.

For almost any given profession, I would expect an unequal number of workers by gender. To the degree that the observed ratio differs from what I would predict, there lies the surprise. Computer programming is a strange activity, and shares enough in common with other male-dominated engineering fields that I wouldn't be surprised that it is equally male-dominated.

One of the reasons I think that programming is such a tilted activity is that it is a really weird activity. By what strange circumstance did monkeys descend from the trees to formalize logical constructions into software? Given how strange it is to adapt biological creatures to this task, you would expect outliers to participate in the task- it is not unusual to expect the personality differences between genders to dominate in who participates, when the outliers are the only individuals who participate to start with.

Regarding the warrior example- I would argue that even if we all fought wars with robots, such that physical stature was irrelevant, men would still self-select to become warriors (robot-pilots) more often than women. On the OCEAN model, men are less agreeable than women, and across the most cultures of the world, men are more agressive than women. This will likely remain true for millenia.

I'm presenting most of my arguments here amorally. I think the reason you moralize my arguments is that they are construed as justifying existing oppression by gender. I do my best to judge individuals as individuals. I cannot pretend to deny the existence of larger patterns while judging an individual, but I can understand that they will influence my judgement no matter how hard I try. To pretend otherwise is blinding myself. To the degree that I broadcast these opinions, I hope to do so in a way that leads people to only judge other groups in accordance with the predictive power such judgements can actually afford, to hold such judgements weakly, and to always understand that variation between individuals is critical more than anything else. My manner of thinking does risk failing to fight the good fight against oppression- however, I think most injustices in the world are cases of individual conflict, and tinting the daily conficts I resolve on a daily basis with overtones of wider societal struggle does more to confuse than clarify.

My main remaining question to you- if you take my last paragraph in good faith- is whether you think that my manner of thinking can yield good results.