In my area, most clubs with that kind of arragement work the way @ComradeEchidna@hexbear.net describes. They simply replaced the signs on the door with a description which plumbing is installed there, which is all people need to know. Which plumbing i have installed says nothing about which bathroom i want to use and it's really nobody's busyness to begin with.

From my experience, in largely cis but kinda woke-ish spaces, that kind of arrangement still means people pick bathrooms based on their binary assumptions about gender, whereas in the really queer spaces, everybody just goes to wherever is less crowded once they've gotten comfortable enough with the place. It's kinda liberating to use a former men's room as a transfem without feeling you're in the wrong place. It's just gender abolition in action, i do not have to care about the bathroom question anymore when i'm in a space like that. Would be completely unthinkable for me in a cisnormative environment.

No reason they have to go just because its gender neutral, people can simply choose not to use them. Depends on the setting I guess, larger venues with multiple stalls and urinals in a common area with the sinks will be harder to adapt, slightly?