I certainly respect a businesses right to most things, but it stops at endangering my life or that of my family. I believe I have a right to self defense, anywhere I happen to be. Let's be real here, we aren't talking about forcing the business to get rid of the sign and allowing a weapons free area, we are talking about taking the calculated risk that you won't have a reason to display your weapon unless it's in defense of life and limb, and willing to accept the consequences either way.
Here in TN, signs have Force of Law, so you run the risk of arrest just for being in the business that is posted, no trespass notice is required. If there is an alternative to the posted business, I go there, if not I will make the decision whether to disarm or break the law. The good thing is, that if you are forced to defend yourself in TN, and it is deemed a good shoot, then no other criminal charges can come from that.