Now here's the thing. As a customer, I have no problem with the supermarket installing a camera and no objection to their telling me about it.
The mistake, however, is posting a sign with a plausible-sounding reason, instead of just telling the truth. After all, what exactly are these cameras protecting me from... a riot in the produce section?
Your clients and customers aren't stupid. It's a lot simpler -- and loads better for your reputation -- to just level with them.