I've seen dogs at both the Wal-marts I shop at here in San Antonio. Both times I asked the owners if they had ever been asked to leave and one owner (a young girl) said she had never been told anything. The second owner (a mature woman) gave me the spiel about her dog being a service dog and by law Wal-mart could not question it. Her dog was not wearing a vest, but she said she did have one for him, he had just outgrown it
In both cases the dogs were sitting very well-behaved in the shopping carts. I don't have a problem with it.