It certainly going to depend on how the person looks. The photo example you provided is a good one. Certainly looks like a man to me. I agree it is stupid, but I understand how a dude out with his daughter does not want some obvious dude wearing a wig and a dress as an "excuse" to go into the woman's washroom.
Actually, I do not know how "public" is defined in these bills. Maybe they cover a washroom on a campground that is generally made available to the public?
If the person in the wig and the dress assaults someone, it's
already a crime whether they're trans or cis, gay or straight, etc. Why are we so worried about what genitalia they have?
If they don't and instead they just use the restroom and leave, what's the issue here?
You said earlier, " It is easy to say to wait for someone to be attacked in a bathroom to call the cops."
Is there any other way this has typically happened? Are we talking about Minority Report shit right now? How else would you report a crime other than to report it when it happened? This is exactly why they want someone using the bathroom corresponding to their identity to be a crime - it's criminalizing someone's existence, and they think that someone is gross and weird.
I'm curious which you think is more likely: a trans woman assaulting a child in the women's room, or a trans woman being assaulted by cis men in the men's room?