I can't speak for every state, and I'm sure you'd get less sympathy in some than in others. In California, if you advertise something for sale, you can't arbitrarily refuse to sell it to somebody. Reserving the right to refuse service to anybody does exactly that. Kicking somebody out because that person is causing a disruption is warranted, but simply deciding that you don't want to sell something to somebody, and presumably selling it to somebody else, is false advertising. Also, it makes little sense to refuse to serve somebody arbitrarily.
There have been cases where people have sued on principle because they don't like signs that refuse to serve people without shoes. Claiming that the Board of Health has such a rule doesn't help, since they don't. It's fine to have a consistent dress code that assures a certain level of formality, but allowing sandals or dirty shoes but not bare feet is something different. In other states, I can see a judge tossing something like that out faster than a person can make an opening argument. It all depends where you live, but there should be a sane reason why you won't sell something.