The law in NC is that it must correspond to your birth certificate, right? So couldn't you kick ANY woman (or man for that matter) out unless she happened to have her birth certificate with her (as opposed to another form of government ID)? From what I understand, different states/countries have widely different regulations on how/if you can change your birth certificate. If you even have one.
And I couldn't name a single time in my entire life when I had my birth certificate with me in a restroom.
I think maybe once when I was about 13 and going to Mexico? Before passports were required?