Simple answer? No, never, under any circumstances.
Now, Why?
As a disabled community, we have rights....That being said, Non Disabled people have rights too.
And, even tho I am a dog lover, I think it is positively disgusting that a person would put a dog in a grocery cart of any type. Whether it's a grocery store, or anywhere else for that matter.
Even at a pet store, I would not put my dog in a cart, because of other dogs previously----do you know for sure that the dog before was dewormed, etc......Do you know that the dog in that cart before your dog is clean of disease.....
Now, let's take it step further......
Personally, I don't want to put my groceries in the cart, after your dog has been in it....Period. No ifs/ands/or buts about it.
"Yes, but I keep the dog in a carrier, or put a blanket down" You cry...
Doesn't really matter to me, I still think that its disgusting and that it seriously misrepresents service dogs to the non-dog loving/owning public. And, again: THE PUBLIC HAS RIGHTS TOO.
They have the right to expect that their lives are able to continue with reasonable normal human social behaviors....and that doesn't include a dog in a grocery cart.....
Now, what to do? If your dog can't be on the floor----after all it has 4 feet, then put it in a sling pouch and carry him/her at your chest....Otherwise, leave him/her at home, or with someone in the vehicle, or on the floor.