“What’s the problem with that?”
Let us start with discrimination, these businesses are OPEN to the public, they cannot legally enforce something they cannot see. If they do not want guns on their prem, let them install metal detectors and and run an airport TSA security system.
If carrying concealed, correctly no one will ever know.
We may differ only on terminology. I would call discrimination if the policy said "no blacks" or "no cripples" or "no people with blue eyes". But "no people carrying boom boxes"? "Obnoxious t-shirts"? "Barefoot"? That's not discrimination per se because the prospective customer can easily leave the boom box at the door, cover the t-shirt, or borrow a pair of shoes. High-end restaurants typically have rentable ties and jackets in case you arrive without one. I don't have a problem with dress codes.
Yes, if a store owner wants to keep guns out, he should install detectors. Otherwise, I'm liable to walk in with my gun concealed, if I want to. Although frankly I'd prefer to spend my money in a shop that respects my RKBA better.