Business people in the United States have traditionally had the right to serve whom they want.
Starting in the 1960s, however, our elected representatives decided that people could NOT be discriminated against because of their particular group.
Over time, the legislatures/courts have added more protected groups to that list.
We are all waiting for the Supreme Court to tell us whether a baker has a right to refuse to bake a wedding cake for a gay couple. (I am guessing that the Court will rule against the baker.)
On the other hand, I assume that the baker, for example, would have the absolute right to tell a customer to leave his/her bakery if that customer insulted a woman customer because of her religion. In other words, rude customers are not yet on the list of protected groups.