I'd be sure and make certain that they understand that by incorporating their own personal anti-gun policy, even though its not state law, that they will be losing business. I'd even maybe mention something like a possible scenario that you could use just as an example of why you wouldn't want to be there unarmed and unprotected. Like maybe I'd say,
"Even desperate bank robbers know there is a VERY stiff prison sentence for armed robbery of a bank. So someone who is desperate enough to rob a bank is surely desperate enough to not care whether they have to shoot the teller or clerk or the little bank manager or any innocent customer in that bank if it means they can make their getaway with the cash. Although bank robberies may not be COMMON occurrences, they DO happen in this country, and people do sometimes get hurt and killed in the process. Playing the odds and simply 'praying' that a scenario like this never occurs in my own lifetime is a gamble and one that is not worth the risk."