Most professional sports I know of (in the US) technically don't have separate men leagues. There are women only leagues, and leagues open to anyone. There is no rule preventing women from playing in the NFL, NHL or MLB. But in practice if you don't enforce a minimum % of women players like I've seen in some amateur mixed leagues, it makes them men only.
The Olympics does split into men-only and women-only, I think.
Hey, not taking sides here, just saying it's not as simple as reducing to people who think women and men (or female and male) are actually the same.
But if it helps taking sides, from our current way of doing most competitive sports, it makes sense to split into male and female (biologically speaking, at birth) and transgenders shouldn't compete on the other side.
For sports specifically, it is worth listening to this Megyn Kelly podcast episode where she speaks to two girls affected by this issue in high school sports, as well as two sports biology researchers - one of whom is trans - discussing sex-based differences in sports: https://podcasts.apple.com/us/podcast/the-trans-athletes-deb...
In depth, balanced discussions around this issue are also difficult to come by because of censorship and vitriol. A good listen on this facet of the issue is this interview of journalist Abigail Shrier, whose recent book drew the ire of TRAs: https://www.honestlypod.com/podcast/episode/3054d6c7/courage...
The only thing I have certainty about is that the people who seek to shut down others, or censor debate, or get people fired, or distort/lie are on the wrong side of things. There are large numbers of people who engage in these illiberal actions on all sides of this debate.
The media and many others are backing transgender men entering multiple women's sports like it's not a problem. They're even ok with it happening in MMA and it's terrifying. You're going to have woman killed with this sort of stuff.
https://nypost.com/2021/09/11/transgender-fighter-alana-mcla...