TL:DR: There is no law that states that you have to interact with them. Leave before they get started if you can.

It is a perennial problem. How can you get people to leave you alone when you are out with your fearful, anxious, or reactive dog? There you are, out with your anxious dog, minding your own business. You went to a secluded spot. On a rainy day. And at a time when nobody else should be out. But here comes that person with the “All dogs love me!” look. Or the “I’m about to give you ridiculous advice about training your dog, whom I’ve never seen before” look. Or the “Can-my-kid-pet-your-dog-here-we-come” look. These folks often have this inexorable zombie walk straight at your dog and just Will. Not. Stop.