Oh, how I wish we had the law (more) on our side here. There are laws, of course--national laws as well as state-specific laws banning "non-service animals"--but unfortunately in Florida, the laws are not enforced equally. Governor Scott passed a law where the owner would have to pay a small fine and the business could ban them, but unless a cop is right there in the store there's not much the store can do because the store owners/managers are too afraid of 'creating a scene' or having some *&(@# write a nasty, one-sided letter that might get them demoted. A policeman or other law enforcement can be the bad guy, but the store owner don't have the backbone to stand up to these people.
I do know that the $hit hits the fan if that dog is in the store when a health inspector visits, though. Unlike the store owner, that inspector doesn't care about hurting anyone's feelings because...well, they're from the government and don't have to be nice or understanding.

A grocery store in Tampa got shut down for 48 hours when such an event occurred, but I doubt the dog owner cared one bit...it's all about
them, y'know.
Several years ago a woman was asked to leave a Publix supermarket in Florida because she brought a pet dog in with her--so she immediately sued Publix for causing her "emotional distress" (translation: embarrassing her in public) and WON a small settlement. From that point on, all Publix said they would do is ask "What service does your service animal perform?", not "Is this a service animal?" or (what I'd ask) "Don't you understand it's a health-code violation to bring your dog in here?" They totally caved and since Publix basically owns the grocery business in Florida, others follow their lead. When I shop and see some old lady trucking around her little poodle/shih-Tzu/rat-dog in the cart, I look at the dog as if he has three heads just to let granny know little Fifi ought to be home.