On rare occasions, I see dogs tied up outside of stores, usually convenience stores like 7-11's and such. I think it's irresponsible for dog owners to do so but technically...an animal is their property and what they legally do with their property is their business. A myriad of bad things could happen...someone could untie the dog and set it free (getting hit in traffic, etc), steal the dog, abuse the dog, dog could bite someone (seen that happen) or feed the dog something that's bad for it.
Around here, the self-absorbed idiots take their dogs into the grocery store (regardless of signs to the contrary) and either put them in the cart or, if they are larger dogs, walk them on a lease.
I like dogs but I don't want them in the grocery store and I damn sure don't want them in the cart. Publix has recently posted signs prohibiting animals in the store except for animals allowed by law. No more chihuahua "guide dogs" with fake, internet bought, jackets.