Well, I live in much smaller country, I've never heard of a dog stolen here before, only farm dogs that live outside 24/7.
If its a small store and I don't see many people around I sometimes tie him outside and just rush in buying what I need and out again.
Stores here don't allow dogs, and OFCOURSE same goes under small and big dogs, dogs are dogs

! No matter what size.
I though can bring them in to one small food store here, but no else I think.