Here is a recent Pew Research piece...

...that I believe is fairly nuanced; that is, it goes towards, if not completely to the bottom of, some of the statistical nooks and crannies you adverted to. Gender pay gap in U.S. hasn’t changed much in two decades (Pew Research, March 1, 2023).

I understand the fact that it depends on what occupations are held by men versus women, but to some extent--not completely, of course--this begs a question. Why aren't there as many women who are commercial real estate appraisers or aerospace engineers? Do they just not like the idea of the job? There are many, but not close to matching the female proportion of the general population--far below, in fact. This gets into societal expectations, too, and while that might be a different discussion for the point you're making, it's part of the one I'm making. And I'm not saying this out of any political motivation. Also, the pay gap was only one element of disadvantage I mentioned.

As for LGBTQ folks, maybe what you mention is unfair. Or maybe the whole system of gender-based sports participation could evolve a bit. If you take the complete set of cis-men and cis-women athletes in any given sport, there will be some men who underperform relative to some women and vice-versa. Also, I tend to think that the incidence of these sports-related issues is pretty low and probably less important to society (or even LGBT people) than we might think.