High heals were originally designed for men in France; I think, if I remember correctly, Louie 14 was pretty short, but, yes sartorial norms change and swing like a pendulum. I don't really know anything much about transgender people, I've only know three and none well. Two were males dressing like women and one was a woman dressing like a man; I have to say the woman dressing like a man was much more convincing than either guy. The guys hands, 5 o'clock shadow and voices were dead give a way's.
But, being hetero sexual all my life and not the type to "settle down" when I was younger; the upshot is I've known quite a few women quite well. And though it's hard to imagine more polarized thinking than die hard conservatives and liberals I'll call bull**** on men and women's thinking being closer; "Men are from Mars - Women are from Venus" wasn't written because "stereotypical" men and women are the same … in any way. We definitely behave like we're from different planets; my observation has been that men and women are so different I'm surprised we have babies when we breed.
I'm sure a survey could be designed to hide the gender of respondents and vice versa, but your statement; "if I gave someone a stack of anonymous completed surveys that measured factors of personality, intelligence, aptitude, and values, there is very little chance they would be able to sort them into a pile for men and pile for women based on the results of each survey.", would be highly survey dependent. I'll wager any statistician or psychologist would agree.
I don't know what to make of your last sentence, it sounds important; but I fail to find any significance.