I love animals, too. As long as they’re well-mannered and well-groomed, which this rat was, I wouldn’t personally have any problems with it. I wish there were a way to somehow get “well-mannered, well-groomed pet” licenses that would make it okay for those pet owners to bring their pets into more places.
However, it’s usually illegal to bring pets into places which prepare and serve food, at least in the US—excepting very specific situational exceptions, and excepting service animals. (For other stores, I believe it’s usually under the discretion of the store owner… Though I understand when store owners want to save themselves from the gamble of “will this pet be rowdy or make a mess?” even as I wish it were different.)
I had been told that the food place can be held liable for a health violation if they allow a pet to remain, and someone were to complain to authorities about it. I had been told it can even lead to them losing licensing… And for that, I have a huge issue with someone bringing a pet into a store. (I couldn’t find any language about that specifically when I quickly searched just now; most of the information I found was focused on what the pet owner could or could not do, and not on the store’s responsibilities. I did see some articles saying the pet owner can charged with a misdemeanor, were someone to pursue it.)