I wouldn't anyway because I know precisely why there are separate bathrooms for men and women: because men usually pee on the seat. In the case I would have to pee in women's toilet, I would sit down (because
what you actually do is eventually respect, not your herd signalling, or empty words).
On the other hand, how many different toilets should there be in your world? Should non transgender women be allowed in women's toilets? That has been an actual question and an actual problem to solve in the world of infinitely exploded communities of precious snowflakes (in the very same order of absurdity, should veiled white women allowed in "coloured women only" meetings? what about transgender black women?).
As food for thought, if you believe that, as a white cis male, I'm a born oppressor, I've also been actually harassed, publicly humiliated, attacked and beaten for being "a fag" (you know, long blond hair), because homophobes don't really care about who you actually are, and also beaten for defending women harassed on the street (because machos/sexists are also generally violent).
In the global competition for victimhood, nobody can win. Who knows what humiliations RMS was subjected to for being ugly, fat, an asocial geek, etc. Maybe he used the power he has in some sets and circumstances in despicable ways. But so do the students at Evergreen, because that's just what human beings do. Being an aggressor or a victim is mostly circumstantial for most people.