he or she may expel you from that property for any reason that he or she sees fit.
Really? And here I thought that the "no coloreds" signs were illegal.
Property rights are mostly codified rights, and they can easily be legislatively modified (with a few minor exceptions) Just like the Civil rights act bans discrimination against race, religion, etc., a law can be passed allowing concealed carry, and prohibiting a business that is open to the public from barring people on that basis. There is nothing in the COTUS preventing such a law.