To put it another way - look at the other examples that have been raised here: the racist CHL instructor and the racist shop owner. In both cases, you've said that these people have the right to discriminate against anyone they please. But here you seem to be fine with the idea that a person who discriminates according to their preferences could be liable, after the fact, to the person against which they discriminate. So what if it were the case that, at common law, there were a cause of action for the wrongful denial of services, which could cover acts of invidious discrimination such as these? Would you object to such a cause of action, as being essentially illiberal?

And, if not, what if the state were to create such a cause of action, by statute? (Which it can and often does.) What then?