I have, a couple times, gotten a tad ticked off at this myself. Mostly it involved poop in aisle 27 at Home Depot. I complained to the store manager, telling him I was deathly allergic to dogs. If the person has a legitimate service animal then I'll leave, but if it's just a con could you ask them to leave? Every retail manager is aware of this issue and they all have a policy to follow.
If the person can't produce proper documentation or explain why that's anything more than an Amazon vest then they have actually asked them to leave.
But I can be an unpleasant, cantankerous, confrontational individual at times. If you don't believe me, you can ask my wife! She likes it when I'm that way taking care of her stuff, not so much when I just go off.
The local Lowes stores allow dogs into their stores, not just service animals.