North Carolina recently passed a law that requires all people, including transgendered people, to use the bathrooms associated with the genders listed on their birth certificates, and that prohibits local governments from protecting transgendered and gay people from discrimination. The ACLU filed a complaint in Federal court to seek a declaration that the law was unconstitutional under the 14th Amendment, and the enjoin enforcement of the law.
The ACLU seems to have an extremely strong case here. The Supreme Court struck down a nearly identical law (though applying only to homosexuals rather than transgender people) 20 years ago in Romer v. Evans, 517 U.S. 620 (1996). Since then, the Supreme Court has never once sided against a party claiming that they were being discriminated against on the basis of sexual orientation.
The complaint also seeks suspect classification for discrimination on the basis of sexual orientation and gender identity. This would make it harder to pass laws discriminatory against LGBT persons, because those laws would have to further a substantial government interest, and be narrowly tailored to further that goal. The Supreme Court has never ruled as to the standard of scrutiny used for discrimination on the basis of gender identity, and its latest opinions on the issue of discrimination against gay people have been unclear as to the standard of scrutiny used; see Obergefell v. Hodges, 576 U.S. ___ (2015); United States v. Windsor, 570 U.S. ___ (2013).
The ACLU is also making substantive due process claims, but I don't think those will be reached. Their case is strong enough on the equal protection issue that it is hard for me to imagine that the law will survive the circuit court. Romer v. Evans, as precedent, is far too on point for the law to be upheld, and because Romer v. Evans only used rational basis analysis, the courts would have difficulty upholding the law no matter how little respect they have for the rights of LGBT persons.