I'm not going to go into depth on this and create a hassle, but unless it's a service dog, it doesn't belong in a store other than a pet/pet supply store. The size of the dog doesn't matter.
The store owner/manager is responsible for the safety of his patrons, and a dog in a store could compromise this. And I'm not talking necessarily of a dog that may bite. All a dog would have to do is slobber a little, the owner doesn't notice or clean it up, someone steps in it and and slips and falls. LAWSUIT!!! And it's the store that takes the hit - not the dog owner.
So - IMO - it is irresponsible for anyone to take a dog in a store, without good cause.
My state may be a small state, but stores here are smart enough to cover their back sides and not allow dogs in stores at random.