I have a brother with Aspergers. One of the best things my parents did for him was drum into him a set of 'do's' and 'do nots' for social interactions. They always prefaced it with, "I know you don't understand WHY, but this is how it is." Before we went to different social functions they'd sit him down and say, "Right, so can you remember what we don't do/say/talk about?" Now, he sometimes still doesn't 'get it', but it's become rote behavior, so to speak. At home, you're free to be yourself. In public, there are certain things that you cannot do with making people feel bad/uncomfortable.
You could tell this boy straight up, "We will not discuss *these things*. We you see us in the street it is fine to say hello to us and the dog, but please don't follow us. You might not understand why, but those are our rules."
My brother, and his friends on the spectrum, just want to get along with people. They really mean no harm whatsoever and often become very upset and confused when people they thought were 'friends' sudden snap at them. They also don't 'get' subtle hints or 'leave me alone' body language. A polite, kind, but very firm black and white statement is what's needed.
It took my father a long time to understand that when my brother wanted something, ie tv time, that my father wanted, saying, "I was watching that and enjoying it, but if you really feel you have to you can watch it." PA, yes, but most people would understand that my father really meant that he'd rather not stop watching his program. To my brother it was permission to change the channel. Then he'd get upset when Dad reacted badly, because he didn't understand. "Not, now I'm watching this. You can have it after." Made brother wander off happily to do something else.