Freedom goes both ways you ding dong. A store owner has every right to ban non-service dogs from their store. Don’t like it? Not the store owner’s problem.
Probably where the animal interfere with the work? Imo doesn't matter what kind of animal you bring as long as it's not a nuisance. The line isn't drawn by species but behaviour
I.e got a chill duck that just hangs around that's fine. Hyper puppy that chews on cables and pisses on all the plants, not so much. As for a hippo you would have to check the buildings structural integrity.
Working retail I never enforced the no dogs policy. We actually did have a lady bring in her bearded dragon. She let me hold it. Ironiclly the only animal I wish I could have kicked out was a legally blind woman's service dog. It's a loud and vicious chihuahua. That little guy is such an asshole. It barks at anyone who walks past it.