I don't disagree with any of that, but I would say that "trans women are women" is about gender, not sex.

It's unclear whether sports are segregated on gender or sex lines, but the historical record leans more toward gender segregation than sex segregation. I honestly don't care enough about any sport to really know the correct way to organize a league, but I do want trans persons to be able to participate in public life, including sport, as safely as anyone else. I'd mostly be in favor of no division based on sex or gender, but people that are more interested in sport than I tell me that's bad and unsafe.