Yep, I hate when I have to make that choice and prefer to avoid public restrooms if possible. I have only been in women's restroom once (because my 4 y.o. daughter got Nature's call and I just could not muster the inner strenght to take her to men's). Nobody said anything though.
Usually, when on my own, I go to men's room and sometimes I get surprised stares, sometimes they double check the sign on the doors and sometimes they dont care. I tend to pass as cis-female most times, but I dont wear makeup, accessories and my clothing style is a mixture between sporty and urban active (no purse). And sometimes people gender me as young guy (especially if I have baseball cap and all my hair is tied up).
The logic I am following is, if women might have an issue with me, they might call for security and that can bring trouble. Guys either wont say anything and just look, or say something which I would simply ignore and shrug off - they will never try to make a huge issue or call a security. That does not mean that I dont feel like a spy or hostile alien in men's private spaces... but I also feel a bit like a fraud when entering women's room too.
Gosh, I somehow missed the title part which said about identifying as M

. Sorry, guess, the above post was not not very useful then.