I, too, have heard from my SO that us using the ladies restroom is disconcerting and some women vehemently object, especially is children are present. The latter fear no doubt arises from the common misconception that we're all perverts and child molesters. I always point out when this discussion comes up that I've been to many many sporting events and concerts where women have walked right into the men's restroom, gone into a stall, done their business, and walked out -- usually under the explanation that the line at the ladies room was too long and they HAD to go. That comment is usually met with a blank stare and a "so what?" response. Here we have slammed head-on into the female prerogative.
My my advice here is, know both the law and the usual police response to complaints about us in your area, have restroom situational awareness, be realistic about whether or not you pass, be careful, don't talk from the stall (your voice - even if it works when people can see you - will likely give you away if you and your femme presentation are out of sight) and most importantly, keep feet pointed in the right direction and together - no man spread in the stall - do your business, wash up!!, and leave.
YMMD (your mileage may differ)
Oh, remember that a momma bear will do anything to protect her cubs -- including claiming imagined facts if the police are called.
Rhonda
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If it's a single restroom, regardless of how the sign reads, no problem as there won't be any women or kinds in there with you to complain about you.