Ok, let's expand the question a bit then. Suppose we change the parameters a bit.
Would you object to sharing a restroom, public or private, with a transsexual woman? Say, one of these women:
I do share a restroom with a transwoman, the downstairs restroom restroom at home, and whenever Sissy and I visit a public restroom together. It's never occurred to me that this should bother me.
Gilda