You bring an interesting point, at least in today's society.
In my state, if you are a business open to the public, then concealed permit carriers are within the law to carry concealed on that property where the general public is allowed. Can a store owner throw you out and give you a trespass warning because he doesn't like your looks? Probably, unless you're an obvious "protected minority" class...
So... a truly private property owner in my state has such a right to forbid anything he pleases (no... no tattoos allowed), but a property owner who declares his property open to the general public does not, at least in terms of the concealed carry laws. Interesting situation, eh?
yeah, that is kinda screwy.
one way to end-run that bit of idiocy is to charge an entry fee to the premesis (sort of a "membership fee), which makes the place a private "club"