that said, this is a subtle issue and you'll find less uniformity on it than you might think. i'm going to share my logic, because it's sort of ironic.
public washrooms are inherently gross places that most women prefer to avoid. squatting in public is just a "yuck" thing. so, if you ask around, you'll hear a common opinion amongst women: when forced to deal with public washrooms, i wish i could stand to urinate. now, as it happens to be, i have the ability to stand to urinate. no woman would ignore this, when faced with the obstacle of a public toilet.
but, i consider it rather disrespectful to walk into a woman's washroom and urinate standing up. this question of "passing" is sort of silly; if somebody is looking at me closely, they're going to pull out the adam's apple, at the least. it's not a function of my projection so much as it is a function of others' perception. i can't control that. i can fix a percentage, a likelihood. but, it's inevitable that some percentage of cis women are going to notice, and consequently inevitable that i'm going to be "outed". to me, the more important question is that i'm following conventions when i'm in there, out of respect for the security and comfort of others. that means no peeing standing up in the women's washroom, or, put another way, that i will squat when i decide to use the female facilities.
often, though, the idea is not appealing. i've walked into the women's washroom, got a good look at it and walked out into the men's room. but, this is something any woman would do if they only could! and, i generally default to the men's room, even if i'm wearing a skirt, as a result of it.
that's a different logic. don't generalize this and apply it. rather, the point is we're individuals and generalizing is dangerous.
as others have pointed out, my preferred solution would be one bathroom stalls.
ironically, again, i'm more likely to bite my tongue and squat when i'm in a more conservative setting, and don't want to confuse people or get into an argument.