The no guns sign can address one, or the other, or both. If the sign says no concealed weapons it means just that, if it says no firearms it means both, if it said no openly carried firearms it would mean that alone.
Do not ever find yourself wanting there to be a law that says the signs can not be there, as much as I hate em, I love what they stand for, rights.
It is no different than your own home, you can choose to allow others to wear firearms or not, you sure as hell do not want the government making that call for you!
The only arguable point one could have would be "public access" and I suppose I would have to agree, if you offer public access, it could be said you must allow constitutional freedoms. There in lies a problem though, if you open "bob's widgets" the government should not force you to allow "mike" to stand in your store saying "bobs widgets suck" just because mike has the freedom of speech. IMHO the government should stay out of it.
Now if we could just convince 100% of firearms owners NOT to shop these establishments, we would see change. When we talk about the sign not having any teeth of law, it makes others think it is no big deal to shop there anyway and they give their dollars to those whom oppose their views on firearms and in the case of some like schnucks, they hand their dollars to those whom gave significantly to the brady's to defeat them.
Rules:
1. keep the government out of it, they never do it well at all.
2. never put your views aside, but always allow others to have theirs or someone will try and take yours.
3. remember the freedom of speech and express yourself and views, value it above all other rights as it allows you to identify the stupid people.