Transgender people make up less than 1% of the population.
I would guess that 1% probably also describes the number of creeps who hang out in bathrooms to peek at someone peeing behind the closed door of a stall. Most people enter a bathroom for reasons other than voyeurism. I know of several women who have used the men's room because the line outside the women's room was too long. No arrests were made. No complaints. No one got upset. When you gotta go, you gotta go and most people understand that.
Politicians want you to believe that any "man" who enters a women's bathroom is there for nefarious purposes. I would be willing to bet that the number of men who have assaulted a woman in a bathroom is less than 1%.
I would suggest that we just do away with sex/gender markers totally. Other than for medical tests and treatment, they serve no purpose except to segregate people into little boxes with labels.
If anyone is in any room for purposes other than using or cleaning the facilities as intended, that person (male, female, or other) should be confronted and told to leave. They have no business there.
It's just another example of society portraying women as weak, vulnerable, and inferior to men. But I have two ex-sisters-in-law who would have no problem bouncing a creep off the premises. My dad describes them as "big enough to go bear hunting... with a stick." Many women are not weak or vulnerable.