Single sex gyms, fine. Closing down public facility for single sex events, not fine.
Heterosexual marriage only bakeries, photographers, caterers, fine. Homosexual ditto, fine.
Single sex haircutters, fine. Muslim only, or one race only, difficult territory. But do you want someone cutting your hair who doesn’t want to cut your hair?
Kinda what I was thinking ... particularly when that someone has access to a straight razor. That said, pass the popcorn -- this ought to be a good fight :-)