No mayor’s role is to represent every single person in their jurisdiction.
That is exactly an elected official's role, inasmuch as possible. That's what his or her constituents deserve.
What about the Local Pedophile Society? What about the Make Soup from Puppy Spleens Society? What about the Demolishing of Heritage Properties Society?
Since those organizations don't exist, we can safely ignore them.
But 2SLGBTQIA+ people DO exist, and they vote and they pay taxes, and they deserve representation regardless of anyone's personal views. Just like fundamentalist Christians do.