Yes. They can ban people wearing blue shirts, if they want to. They can ban lefthanded people. Its their property, they can do, pretty much, what they want and ban, pretty much, what they want. There are a few, special, protected classes of people and things that they cannot ban. Carrying a gun is not one of them.
Businesses are not empowered to make laws. These are not laws, they are rules or policies that private property owners have established for what they consider proper or acceptable conduct on their property. You get to make the rules on your property and they get to make the rules on their property. You can't tell them what you, or they, can do on their property.
Most states, that I know of, have very similar laws on this subject.