According to this 2016 article it's not prohibited by the federal government, but is prohibited by some state governments. Essentially it's the same protections as other characteristics such as race, gender, sexual orientation, etc. just with different states defining different characteristics.
Incidentally I think this is one of the weird things that both sides agree on contrary to the law - if for different reasons. A lot of Democrats (though I'm sure not all) seem to like they'd like to refuse service to any Republican/Trump supporter - while a lot of Republicans would argue a business has the right to chose who to do business with because of freedom of association.