Isn't this kinda like the Luby's case in Texas from way back when I was in grade elementary school?
If you're referring to Killeen, Texas, I'm not sure how you make the two connect. In that case, Texas law at the time forbade carry of handguns by anyone who didn't have a badge. Result: lots of people were killed when a madman drove his truck through the front of the restaurant and got out and started walking around the room, shooting helpless patrons in the head. Dr. Susanna Gratia Hupp was in the restaurant with her parents, both of whom died, in part because she had decided to allow the law to disarm her, and left her gun in her vehicle.
Contrast this with a situation where the law says you can carry, and a business is allowed to forbid you to do so on their property, but is liable for any injury you suffer as a result of that policy.
From my perspective, yes, the business should have that right, though governmental entities should not have that power. If the business is preventing you from protecting yourself, they bear the liability for injuries resulting from that decision, just as they would if they failed to put out a "wet floor" sign and you fell because you didn't know someone had spilled something, or they'd just mopped. Another analogy would be if they did not require hearing protection in an area with known loud noises, or eye protection if that is needed. If they have a reasonable means of knowing of a hazard and don't do anything to mitigate it, that's on them.
What hazard? The one that exists with this sign
Blessings,
Bill