And if I don't?
Do I then get to demand such person prove it?
If not, why not?
Why does -or why should- being transgendered trump basic safety concerns?
There was a case maybe last year or so, when the NC law was in the news where some protective citizen stops someone they thought was a biological male walking into a women's restroom.
They started with exactly the kind of questions you're mentioning, and when they didn't believe the answer, they restrained this person and called the police.
This person happened to be a cisgendered female who dressed andryogynously and had a short haircut and a deep voice.
I don't think there's actually a reasonable place for citizens to be grilling people on their gender or sex.
Trans people are a tiny tiny portion of society, and the vast majority of them who are using facilities of their transitional gender are people who are presenting very clearly as the gender they are transitioning to. So there's not really the precedent of male looking people going in and out of a restroom all day. It's still going to be very very rare no matter how accepting we become.
And despite the "what if" scenario, nothing even remotely like this fear has happened in any of the places that allow trans people to use the appropriate bathrooms. If someone really wants to sneak into a bathroom to assault people, well, if there enough people watching the door to see them come in and question them, then there would be people around if there were an assault. Gender norms for bathroom entrance are not the major barrier stopping a flood of rapists.
That's a bit like saying, if you have bathrooms in a zoo, then the gorillas might get out of their cage and assault someone in the bathroom. Sure it's technically possible, but very unlikely.
Here's something that really happens. Trans people are assaulted when they enter the bathroom of their birth-assigned gender. Trans women are sexually assaulted in men's bathrooms. Given the small population, it has happened quite a lot.
The idea of subjecting a group to real violence, that actually happens with some frequency to avoid a rube goldbergesque speculative risk is ridiculous.