Transgender

That's a good question. First, you'd need to find a doctor that's willing to sign off that a trans girl is of the female sex, rather than that she identifies as a girl. And the fundamental argument they'll make here is going to be that girl's sports are a protected space for female athletes under Title IX, and that Title IX is specifically about sex, not about gender identity, therefore they can restrict who is allowed to play by sex rather than gender identity.

Not wanting to get caught in Title IX is also why they don't place any similar requirements on boy's sports, because current interpretations of Title IX (that go back to at least Obama if not further) require allowing female students to play on a boy's team, but don't require allowing male students to play on a girl's team even if there is no boy's team for that sport. And yes, that is a weirdly discriminatory interpretation of a law that bans sex discrimination in federally funded educational programs, but it's the one the federal government has stood by for a long time).