So we're back to "carry ID always or flash me to use the bathroom". Because that's a reasonable thing to do.This isn't a normal situation, so bringing in normal situations doesn't really work.
We have a case of a woman, that looks and acts like a man, being in a Woman's Restroom. And the cops being called because someone noticed it and asked for their assistance.
Now, these cops have two options:
1. Let the "woman", who might very well be a man, stay in there - and if that's the case, fuck rules. We have separate restrooms for a reason.
2. Verify that said "woman" is indeed a woman. Now, how does one achieve this? By ID; Or physical checking. And I don't think the second option would bode well for the Policeman....
This is not a case of someone having to use ID to go to the bathroom. It's a case of someone, who acts and looks like the opposite gender, being in a restroom and it causing unrest for third parties.
No ID to backup that person's claims (or refusing to comply because ~arm gesturing and shit~ edgy)? Better safe and sorry and wait outside the restroom for the rest of the girlfriends.