The “Alternate Lifestyle” club was not at YU, but rather at Einstein. Einstein and Cardozo are non-sectarian (As is YU) but many students there arent even jewish. They have to obey the New York Law.
If a yeshiva takes government money and a “Person who thinks they are a woman” wants to teach Gemorah at the yeshiva and the yeshiva says no, That person can sue under the anti-discrimation laws of NY and would likely win
There was a “Female Couple” where one of the was at Einstein and the partner wanted to live on campus , YU said, NO and the couple sued and won