I respectfully disagree because that goes against individual freedom. I understand that historically in the US there's been racism but that's no reason to erode individual freedom.
A corporation is not a person, though. It is a "legal person", which is a really unfortunate term precisely because it confuses the matter of natural rights and freedoms.
Now, I would agree with you if we were talking about individuals. In that case, yeah, I think you should be able to refuse service for any reason or no reason at all to whoever you want. But if you go and get a corporate charter from the government that, for legal and fiscal purposes, creates an entity that is distinct from you-the-actual-person, then I don't see any problem with the same government telling that distinct entity what it can and cannot do. That entity has no natural rights.
Now, I would agree with you if we were talking about individuals. In that case, yeah, I think you should be able to refuse service for any reason or no reason at all to whoever you want. But if you go and get a corporate charter from the government that, for legal and fiscal purposes, creates an entity that is distinct from you-the-actual-person, then I don't see any problem with the same government telling that distinct entity what it can and cannot do. That entity has no natural rights.