I do think there are sports this kind of idea will be more or less plausible for. Wrestling, my intuition was, would survive scrutiny for sex segregation, although some interlocutors came at me with counterexamples on that! Rugby also, intuitively. 1/

Re showers, what if the norm simply changed so they were less communal? I am in general shy about sharing showers, although I confess complete ignorance about what role communal showers might play in team bonding or morale. /fin