What the hell do you think is going to happen to you in there?
What already has happened. Perverts (here defined as men, not trans anything, but actual men) take advantage of the new law (which prohibits anyone in a public place from challenging them, if they choose to wander into the ladies room) to have for them a “safe space” where they can shoot photos, or even more horribly have access to children or women for sexual abuse.
Anyone who is familiar with the psychology of pedophiles and rapists knows that this will occur.
Disturbingly, our partisan society seems unable to see the obvious solution to this non-problem. Public buildings must designate a single unisex restroom. That immediately solves the problem in the majority of buildings. Smaller buildings with existing single-stall facilities which lock solve the problem by designating them unisex.
For the tiny number of buildings that don’t fit into the above (they have two multistall facilities) you handle it in the building codes, which should state that all buildings must provide a unisex option. Over time, all buildings will then have such an option.
Until then, (horrors!) the tiny number of people inconvenienced (specifically, the transwomen who don’t pass) might have to find another option.
It is madness to think the only solution is to force all facilities to be unisex.