Suppose some business refused service to nazis. That would be all right because nazism was a violent, totalitarian world domination movement.
Well, there is a group that calls itself a religion but is really a violent, totalitarian world domination movement.
Actually not. You could do so because they aren't a "protected class" under the 1964 Civil Rights Act, defined as race, color, religion, sex, or national origin. So you could deny service to Nazis, but would have a problem banning members of a neo-Nazi church, since it's a religion. The argument of homosexuals was whether sexual orientation should be a "protected class". Some states have passed laws to make it one, and more judges have made up law to do the same.