Kinda...
If the law specifically limits the choice to "birth gender", it does present a small quandary for those who actually have undergone surgery and therapy to alter their appearance and equipment, if they haven't had their birth certificate changed (if that's even possible).
I would propose that single-sex bathrooms be reserved for those who have the sex-appropriate genitalia, and those who suffer from the delusion that they are other than what they are can use single-person unisex bathrooms, if available (and I wouldn't make the unisex bathrooms a requirement).
JMHO.
I’ve actually seen unisex bathrooms described as “discriminatory” by the gender-bending crowd. Which just goes to show that the real agenda here is to flaunt their perversion.