I have never been out dressed long enough to need a public bathroom, but I have been in the men's room at concert events when the women started coming in to use that facility
since it had a shorter waiting line.
That was totally overlooked by the security/police on hand, and for the short time I was there (with my former GF) there were no adverse events.
Everybody just wanted to relieve themselves and go back to the show.
This country, society, (the good old USA) is still way behind the times IMHO.
It really should not be an issue if you are there for that purpose.
I don't see many restroom facilities here in Atlanta for unisex/universal/handicapped.
At least the ones I have been to.
As for sitting or standing, If I did venture out in full girl mode I would hope the women's room looked better than the ones I have seen when I used to work as a sound engineer in lot's of Atlanta rock/disco/techno clubs.
I might want to hover over that seat, or stand.