[Riverman94610]

Do you mean based on personal appearance or ANY reason a business wants to use to bar a customer?
Do they have a right not to serve Jews or Christians?Green Party or Populist Party members?Gays or adulterers?
Please clarify.

[taxcontrol]

If you follow freedom of association, yes. You are free to patronize any business (or not patronize) and businesses are free to choose who to serve.

A private business (unlike public utilities) can target it's customer base as narrow as it chooses. If I only want to sell furniture to people with hazel eyes or jews or whatever, then I'm free to do so. No that I would get much business and my business would likely fail.