Why do you want to other trans people?

There’s alot of other ways you could have divided bathroom use but you ignored race, occupation, sexual orientation, housing status, handedness, whether they support the Yanks or the Mets, if-or-not they wear flip flops, number 1 or number 2, time since their last covid test, attractiveness, their tact when sniffed, and dick size.

Could have segregated bathrooms by any the above categories but you chose to suggest a bathroom for (presumably cisgender) Man, a bathroom for (presumably cisgender) Women, and an “Other” bathroom occupied by people who are not just not men and not women (whose absence of a space “for” them is a salient if side point) but people who very much fit within the binary categories “Man” and “Woman” but you still want separate, with the odd, ends, and enbys, from the Cis People bathroom.

Think about why it is you want a “Cis People Bathroom”.
Don’t even think about the invasion of genital privacy or general propriety required to effect the border you wish to erect.

Think about why this is a thing you want.
Why you want people, who have genders—which are every bit as real as yours—, to have to expel the semi-solid remains of food and wastes and toxins filtered from their blood in a separate room from you.
What is it about these people that makes their shit stink more (or less) enough to warrant their doing so separately?

Surely it’s not as simple as “Their gender turned out differently than a 13-second-old genital exam told them that it should, for which they need be punished.”

Respect if that’s it. “Fuck Trans People.” Not the way I’d go with things, but it’s an ethos.

I don’t think that’s it, though.
You seem nice enough I doubt naked bigotry compels your actions.
You seem well-informed enough—further—to know just how expensive a “fuck you” a third for every second bathroom would be just to keep a percentage point the populace apart 'pon poop and piss.

So if it’s not naked bigotry, and it wouldn’t be very effective bigotry even if it was, what is it that makes you think trans people need to not be around people who aren’t trans during the 15/1440 minutes a day the average ass spends on a toilet?