> It's clear how insane this culture war against trans people is when you consider this only applies to trans women and not trans men?

In most sports, the "mens" division is actually an open division that accepts all participants regardless of sex. Women just don't compete in it because they have no shot at getting a decent placement. The fact that males and females can't fairly compete with each other is the raison d'être of the women's league. This, and not culture war propaganda reasons is why only the most deranged bigots have an issue with trans men competing in "mens" sports.