I kind of see where OP is coming from actually.
I would be surprised if there are not any personality traits that are innately more likely in males, or innately more likely in females.
Similar to the fact that most men are taller than most women, it MIGHT be the case that most men are more empathetic than most women for example, or vice versa.
However, as far as I know we have no way of knowing what innate differences might be in existence, because of the differences in socialisation between boys and girls in all cultures from birth.
Would be interested in anyone who knows of studies that have proved any innate differences one way or the other.
Even if there are innate differences in average personality traits though, I don’t think that should change anything in terms of how each individual should be treated, as the personalities of the sexes will overlap massively.
The danger is that any small innate differences will be naturally exaggerated because young people will be influenced by what they THINK they should be interested in or good at.
Don’t agree with your latest point OP about certain roles/jobs being more suitable for either sex although maybe it’s just the way it is worded. Yes more men will always be firefighters and that is fine, but the criteria should be about fitness/strength, the sex of the individual applying irrelevant as long as the criteria are met.