It is a singularly stupid law.
How are they going to enforce that law?
Some man who considers himself to be female, dressed like a woman and probably looking like one as well, enters the Wal*Mart lavatory, enters a stall, takes a piss or a dump and then walks out.
What sort of person is going to report this? What cop is going to bother to arrest this feminine looking man and demand to see his birth certificate?
When I go into a public lavatory, I pay as little attention to anyone else in there as possible, do what I came to do, and leave. It has not once occurred to me that behind that stall door was a woman taking a dump rather than a man. Nor can I bring myself to care.
Like the "defense of marriage" laws passed earlier, this law was passed with great fanfare to increase the turnout of fundamentalist yokels and hicks at the polls so the better educated people around the Research Triangle area would not vote the yokel governor and his hick pals in the legislature out of office.