Jeez, when I saw Dwarfy so doggedly arguing from a sane viewpoint I actually backed out of the thread to see if there was a "new" button next to the mod log. Phew.
Anyway, to skirt safely around the fringes of this argument, in my experience unisex loos - with a shared bathroom area containing the sinks, even - tend to work quite well, but then I suppose the main place I've seen those is in music venues where everyone is supposed to share a common interest and be excellent to each other, plus there will generally be a security guard not far away.
Still, the question here is avoiding feelings of discomfort, not physical danger (mostly?), and as far as I've seen it goes quite well. Segregated loos involve a whole different mindset where the sight of a member of the opposite sex comes as an unpleasant shock.
Urinals are a useless and inefficient waste of resources and should be phased out across the board regardless of attempts at inclusivity - and no, I don't go out of my way to avoid using them.
On another note: I don't really understand why asexual would count as some persecuted sexual orientation, or why I've seen them described as "out and proud". Like, wtf? You're/they're above all that. Maybe I attach less importance to sexual intercourse than most people, but the idea of someone lacking an idea in sex really doesn't seem like a big deal. And I'm not even a tolerant person like most of y'all! Lacking an interest in alcohol/drug use is far more damning.
Um, I might have had more to say here, but it's getting on and I need to finish my coffee and start panicking if I'm to make lunch, (hopefully) exercise and eat breakfast quickly enough to make it to work on time.