Well, our dog passed away so I can say for sure that in 10 years of taking her with us she never bit anyone. At 115 lbs we were not toting her around in a purse or trying to sneak her in anywhere obviously.
Most places we took her had water bowls set up and treats for the dogs, so obviously the stores and restaurants were fine with them being there.
It's common in my neighborhood, it's not really up to you to decide whether or not my dog enjoyed going on a stroll with us and making some stops. We knew she enjoyed it, since she was always happy as long as we were there. Her enjoyment came from just being around us. (well, mostly dh, she was insanely attached to him) We didn't allow her to go up to people, she stayed right by our side, didn't bark and never had an accident. Again, she has passed away so I can say for sure that she never bit anyone or had an accident.
We did not sneak her inside. The stores allow it, even encourage it by providing for them. My bank has dog treats right up on the counter and water bowls as well. Why should we have left her at home when we were not doing anything wrong? If the mere sight of her across the store may have upset a person here or there, or they did not understand why we would bring her, that's really their issue. Lots of people would come up to her and pet her and chat with us, so there are people out there not bothered by it. Anyone that didn't like her was free to ignore her, why should we not do something that is permitted for a few people that don't agree?
I make no claims of having a service dog, she was just our pet.