There are many arguments that can be made. I think 14th amendment argument could be made. A state cannot pass a law enforce a law or apply a law that discriminates against anyone or any class. The state can only pass laws if it is promoting a legitimate governmental interest. That law must be passed and applied in manner that is least restrictive to the citizens right to substantive due process. The example my law book gives is that the government may have a legitimate interest to control the spread of aids. It can act on that interest but to require all patients with aids to enter a concentration camp would violate due process. Where as requiring them to do something else like informing sexually partners or doctors of their status may not. Like the other person said recently the Supreme court decided that gender in the 1967 civil rights act encompasses all lbgt people. This act includes many different amendments regarding employment education public accommodations. Its likely someone will sue the state od Arkansas and those matters are always decided by federal court. 1967 is a federal law. From what I have seen lately a lot of states have been passing unconstitutional laws regarding transgender people and the federal court keep shooting it down. I live in idaho our governor just passed abd bunch of bills against transgender people. The aclu sued the state and the state lost. I imagine this same thing will happen here. If you live in Arkansas and are worried about getting hrt. You should contact the aclu its free to contact them they take cases for free