I've taken Romeo into Target once and Walmart a few times inside of his bag. I usually just put him on the top part of the cart and most people never even know he's in there. However, I tried to go into Walmart the other day with him and this guy stopped me at the door and told me that I couldn't bring him in.
It was just so annoying because he's so small and wouldn't have even come out of his bag. I don't see what the big deal is as long as he's not coming out of his bag or being brought around food. Some places are so difficult.
On another note, I've taken him to the mall a few times and never had a problem. (in his bag of course)