Hm.  I suppose it varies radically from place to place.  Frankly, I'm shocked that there are actually rules, let alone enforced rules, about who can use which restrooms.  Though I can see it in Alabama.  Several years ago, LGBT groups lobbied to have gender-neutral restrooms made available on campus.  It was a very successful campaign, as they found allies in the droves of male faculty, staff and graduate students with young daughters.  You don't want to take your little girl into the men's room, you don't want to enter the women's room even if it is only in the role of dad, and you don't want the child to go alone.  What to do?  So no we have gender neutral restrooms, with amenities for both sexes and children too, with doors you can lock.  Frankly, everyone likes them, regardless their gender.  I think everyone just likes privacy.

I knew a high school administrator who worked in a school where one of the teachers decided to to have a sex change (I don't remember in which direction.)  They were not only allowed to keep their position; they were allowed to use the restroom they chose.  

I've never heard the sexual predator urban legend.  And I've heard A LOT of stories about sexual assault.  It doesn't really make sense.  If it is a public restroom without a lock on the door, it seems no different than assaulting someone in a public area.  Anyone could witness it.  Why bother dressing in drag?  If it is a single restroom with a lock, only one person uses it at a time, so who cares what their anatomy is?  Lock the door behind you.  I use men's restrooms when they are the individual locking kind, fwiw.  They never have a line.  :)  

"Pretending that you already know the answer when you don't is not actually very helpful." ~Migeru.