I don't take my dogs shopping with me simply because I don't like people touching my dogs. You don't know how clean their hands are. Also, there are a lot of diseases that are air born. True, that's why you should have your dogs vaccinated but what about people that don't keep up with that.
Just the other day, took the pups in for a wellness check. When I was leaving, a mother and her son (around 6 years) were in the waiting room. Boy walks up. I told him (as did his mother), you can look but DO NOT TOUCH THE PUPS. His hands went right in the box to touch them. I was furious. I snatched the box up out of his reach, paid and walked right out. Even my 6 year old knows when to touch and when not to!