Hmmm.... I don't like the idea of trying to come up with lots of new govt rules, it too often becomes infringment of rights, weather intentional or not....
A better way to go would be to allow all animals, but provide the retailers with the right to add fees for bad behavior... ie your pet starts a fight, you pay damages, etc... providing minimal govt involvement, while also ideally preventing the retailers from over reacting...
Another issue is that most restaurants have rules about pets due to health and cleanliness issues, ie pets getting around food, etc...