Personally I won't patronize a store that has a "No Guns" or "No OC" sign if I can help it. I 100% understand that you have the right to put up such a sign, but you must realize that I also have the right to do business elsewhere. By telling you I am letting you know why you aren't getting my business so that you can make a more informed choice as to how to run your business.
Case in point. Brigadoons in MWC has a "No OC" sign. Prior to it going up I talked to them about the subject. Initially they said it was because they didn't want "yahoos" showing off their guns and passing them around and what not. After politely saying that such things don't happen in other OC states (this was while waiting on the OC law to go into effect in OK) and that they could always ask those creating a problem to leave, they changed their story to "it's an insurance thing" which I HIGHLY doubt their insurance mentions OC at all (especially given that at the time OC wasn't even legal yet). Once we were done talking I told them that while I disagree with them, I respect their choice but won't be shopping there anymore. This also meant that I didn't fly a flag for them while deployed as I wasn't going to both buy a flag (they hadn't given me one) and then fly it for a store that didn't fully respect my rights (though I respect their rights to put up such a sign). Almost a year later I went by and they still had the sign, so to me that says that they have accepted the loss in business over their views.
As for you, you have to go with what you believe in so long as it is legal. But also remember that you have the right to remove people who are causing an issue. To me, putting up a sign that says "No OC" says that you don't really support the 2A in its entirety, thus I won't do business with you. What I would do is just not put up a sign and ask anyone who causes a disturbance to leave. Note that if others are offended by an OCer who is minding their own business then THEY are causing the disturbance and NOT the OCer. If your patrons comment on it then either explain to them that what the person is doing is legal and you're simply respecting their rights, or put up a sign and realize that you're risking losing business because of it.
As this is an OC forum feel free to learn about why we prefer to OC instead of CC. While I'm sure for some it is to be "flashy" (even if they won't admit it), for the vast majority that has nothing to do with it.