Yes, they can still post signs, as they are a private business. Refusing to obey those signs is akin to trespassing, a very minor of fence.
My point was, the business owner is able to control his own property. Also, in the event of a shooting incident law suit, the owner can claim not liable,” I put up the sign.”
I’ve witnessed a gun-shop owner tell a cop that no loaded guns were allowed in the store as the cop entered.
Cop responded “but I’m a cop?”
Owner said “I don’t care”.