The primary reason behind 'no gun' policies on business premises is to maintain a defensible position against liability claims. Customer, with or without proper legal reason, pops off a round or two and someone is injured, company lawyers can point to the company policy and signs prohibiting weapons as a means of deflecting any claim against the company. Employee, with or without proper legal reason, pops off a round or two, company lawyers can easily show that the employee was acting outside the employment relationship.
A contributing driving force is the insurance industry. You want our company to insure your business, then you must post these signs prohibiting weapons.
The point I'm trying to make is that, for the most part, your local merchant could care less whether or not you are packing; all he is doing is complying with corporate policies and/or insurance requirements. A business may be open to the public, but it remains private property and the owner/management may limit any activity on the premises as they see fit. When you enter a business your legal status is essentially that of a trespasser with permission to be there only while complying with the owner's rules.
With my sidearm properly concealed I can come and go just about anywhere, with the only exceptions being places with metal detectors for screening. Open carry is another matter entirely; lots of folks will always go a little crazy when they see someone with a weapon strapped on.