Well, do you care if bartenders and wait staff misread you sometimes? Do you want to correct them, but hold yourself back because you don't want to be rude? Or do you genuinely not mind? That's not a question anyone can answer for you.
On the bathroom thing, though, you probably should use the men's if it's not seriously a safety issue (no doors on stalls = pretend you just came in to wash your hands, and go find another bathroom; at best, someone could accidentally see you undress, and at worst, it could be a bathroom where guys cruise for sex, which is the usual reason for door removal, though it doesn't work). If there are doors, you can just go in, do your business, and leave, and it's really not that different.