I am really curious as to why some people don't want their service animals petted. I'm one of those who often asks to pet the dog.
I don't have a service dog. So, this is just me speaking from an animal behavioral perspective - if it's a helpful way to think about it, for you (or anyone). And if not, please ignore me :)
An animal lover will always have an instinctive desire to connect with the animal; and dogs are so wonderful to connect with. You (general-you, not specifically you) want to pet the dog because it will give you a little gift, in that moment. I'm not saying "selfish, selfish, bad!" - I'm saying, it's a happy-making moment, to get to connect with the dog.
The dog has been trained as a working dog. So, no matter the breed, it's in the dog's DNA to want to please. Dogs in training won't be as chill about it as well-trained, seasoned dogs. But they all are interested in giving whatever, when they are asked.
The dog already has a full-time job - and they do know who they work for. They know - or are in the process of learning - that there is one person they truly listen to, and one person only. Their handler.
When you (generic you again, not you-you) make eye contact with the dog, and the dog can read the interest and attention in your face - the dog wants to give you what you want. And, the dog also wants to do their job. The end result is - you are giving the dog an irreconcilable conflict, which is probably not so pleasant for the dog. Depending on the level of training, it is easy or hard for them to reject that happy eager human face. But either way, a distraction is happening. And that happy eager human face thing will repeat itself over the course of a day out working many, many times.
I actually get a very strange jolt of happy whenever I have the opportunity to notice a service dog and be extra good about not creating a problem for the dog. I watch them in my periphery, and am so frankly awed by just how awesome they are.
@Justmehere - you handled that situation like a rock star. I think
@Kefira's thing about keeping the ADA legal contact info business card (if I understood that right) might be something you should co-opt; just for those times when anyone is trying to give you grief - you can give them the card, and tell them to call and register a complaint. Such a thing would probably stop a "do-gooder" up just enough to make a graceful exit, mic-drop style.