Asking. They cannot groom customers of lawfully owned property where public has right of access as invitees. Unless unlawful local or state law prohibits...which will surely die in court challenge. MHO.
Discrimination, too.
In my jurisdiction it is a condition of my CCW permit that I can't carry into a business that posts a sign saying it isn't allowed. But they have to post the sign. Just releasing a statement to the media isn't enough. Without the sign I'm ignoring them.
I don't understand why businesses do this though. Their best course of action is to not say anything at all, because if they say anything on the subject there is guaranteed to be one group of people whom they piss off.