What we need here is a good Dad solution.
Any of the dads of my neighborhood growing up would have approached this sort of fight in the exact same way.
"What the hell's going on in here?!"
"He wants in my spaces!"
"I'm SHE so they're my spaces, too!"
"You're not a she!"
"You can't tell me what i am or amn't!"
"SHUDDUP BOTH OF YA! If you two can't figure this out, we'll just take spaces away, OKAY?"
"Dad, no..."
"Mr. Willis, we didn't want..."
"Nope. Too late. Now there are just bathrooms with urinals and bathrooms without. Got it!?!"
"....yessir...."
"Ya happy?"
".....not really..."
"Well, you had your chance. Now go change the signs on the bathrooms, locker rooms, gyms, saunas..."
"......yes, sir."