Lastly, and more importantly, you do realize that, even if they do have a sign, that sign is about as worthless as the gum you step in on the way to the door with that sign, right? "No guns" signs do not have the weight of law in Florida, meaning, it's not illegal to ignore their precious sign. Basically, in a nutshell, a private person or entity cannot make something illegal by simply posting a sign saying you can't do it.
Even if that marketplace were county or city property, State Preemption makes it unlawful, as, only the State of Florida can legally govern firearms.
And, while I respect your choice to refuse to do business with such places, personally, I refuse to let such ignorance have that much power over me and my actions. Why should I have to get back in my car, spend more of my time and my gas going somewhere I didn't intend to shop because of a stupid sign? Nope, I get much more satisfaction out of tugging on my cover-shirt and giving my Beretta a little pat as I smile and walk right past their %$@#! sign.