I think the OP identifies an important issue having little or nothing to do with gender: Participation in school athletics is not extended to all the kids who want it.
Full disclosure: I’m a former PE teacher and coach, though I left that field many years ago.
As a former sports coach, you may find it surprising that I say youth sports are incredibly, vastly venerated beyond their importance. We make such a damn fetish about youth sports and it’s a lot of nonsense. IMHO what’s important is that kids get to play if they want to. And that’s where we fail.
The solution to the OP’s issue would be school sponsored recreational sports. This need not pre-empt actual athletic teams, but could exist alongside. I’ve seen it done. Some school districts set up rec programs in which any kid can play, period. There’s no cutting kids, there’s no tryout. A kid wants to play, they have a place to play. They can try to earn a spot on an actual athletic team if they want, or not.
That would be a system that serves all kids in the school district. But we mostly don’t do that. We in the U.S. are largely wedded to the competitive sports model above all else, which leads to political problems of various kinds. Which is to say, we don’t really care about kids participating in sports / athletics. We just want want the football team to win, by and large.
I’m also pretty dismissive of the argument that gender segregation / trans segregation is about student safety. If there’s a kid on the high school football team that’s 6’ 8" and weighs 350, they aren’t generally prevented from playing. If he runs over an opponent, well tough, it’s football. Same in basketball and other sports that don’t match people up by weight, such as wrestling.
Even in wrestling, weight matchups don’t even things out. There’s no attempt to match kids up against those of equal strength or other factors.
But leaving all that aside, if we were really worried about youth safety in sports here’s what we would do:
- Eliminate traditional football
- Require soccer players to wear head protection (that sport causes a ton of injuries)
- Regulate cheerleading more rigorously (again, lots of injuries)
If I were king of the athletic directors I’d take the football team budget and create a rec program that served every kid in the school district. I hated having to cut kids from sports teams and I want everyone to play if they want to. Of course, I would never be permitted to do this. I do not miss being in that profession.