This entire "debate" is really dumb and makes the US look stupider and more intolerant than it actually is.
First off, there's no way to actually enforce the bill. To actually enforce it, you'd need to hire people to stand outside of every bathroom and make every person show their ID, which is the biggest waste of time, money, and resources ever.
Second, does anyone actually pay attention to other people in the bathroom? I mean, have you ever really studied the people who are in there with you? No, because that would be fucking awkward and weird. If a transwoman was in the bathroom with me, I wouldn't notice because I don't intensely study the women who are peeing with me (Well, I'd probably notice if a transwoman was like Chris or Phil, but that's extremely unlikely).
And finally, if someone is being a creep in the bathroom, there are already laws that deal with creeps in the bathroom. We don't need another, stupider law.