I voted to keep carrying and go shopping anyway, but it's really more of a 'sometimes' answer.
If it's a business I really need to use, then I'll just keep carrying concealed and go shopping.
If it's a business I don't really need to use, then I'll go elsewhere out of principle.
In my State, the signs aren't enforcable by law. The business owner can tell you to leave, which then it becomes a trespass issue if you don't comply.
The interesting thing with these signs is that many business owners/managers don't understand the law and how it applies to different types of conceal carry licenses.
For example, as a reserve deputy and a license armed PI, I can conceal carry pretty much anywhere (schools, bars, gov't buildings while on duty). The signs on private businesses don't apply to me even off duty.
However, many store owners/managers don't understand that. They think all concealed carry licenses are the same.
This has not happened to me, but it has happened to a fellow PI. He entered a place of business with his concealed weapon. His weapon printed against his shirt while bending over to pick something up, and a manager told him he couldn't carry in there. My friend showed him his identification and mentioned that the signs don't apply to licensed investigators (he even quoted the statute). The manager persisted that he leave. So, my friend left. No sense in causing a scene and getting the police involved when the police have more important things to worry about. Both were polite with each other and went their separate ways. None of us will do business with that place again. He said he was going to write them a letter explaining things, but I don't know if he did or not.
So, whether you're the one carrying or the one telling people they can't carry, make sure you understand the laws in your State. It can help avoid problems.