Chad used to take Zeus in the grocery store all the time and never got told otherwise. Zeus would just lay there, lol. Of course, he's 6'3" and bald so seeing that with a little 6lb Yorkie may have had something to do with it. He would take him into Chipotle all the time too but just stayed quite a bit back from the counter. Manager said that it was OK, lol.
Since we've had Thalia, we haven't really gone into many stores. A few, if we're both together, but without a stroller it's a bit tough.