While I agree that we shouldn't go to stores that don't support our rights, we must remember a couple things.
A private business has rights as well. You can't sue a business for not allowing you to exercise your rights. You can only if they discriminate against a protected class, for example, if they don't let you OC because you are 40+, black, muslim.
I suppose you MIGHT be able to sue after the fact if, for example, it is posted as a gun free zone, you normally carry, you didn't because of the sign and then you get shot by a BG while inside. I assume you could make an argument that the business exposed you to undue risk because they didn't allow you a means of self-defense.
Anyhow our individual rights aren't any greater than the businesses rights.
If you don't like it, don't shop there.
On a separate sub topic of this, I would think that if I OC'ed in F&F after reading this forum, I could defend myself from a trespassing charge by saying I wasn't directly notified of their policy, which I wasn't. As soon as I had the 1st real encounter with LEO or F&F management telling me my firearm was not welcome, then on subsequent visits I would be liable if I OC'ed.