Sports are all about the rules agreed to. Leaving the LGBTQ argument aside for a moment, segregation by gender is basic for without it it’s difficult to imagine large numbers of female participants post-puberty. Now returning to the question of LGBTQ... you can have the legal they can have a legal victory, or you can have girls/women’s sports. But as a practical matter you can’t have both.
Liberalism & much of modern day culture is an exercise in avoiding reality & pretending the consequences of avoiding that reality don’t occur. When those consequences do occur the blame is shifted to someone or something else.