Since "doesn't" is present tense, "presume" also needs to be present tense. Your statement is timeless. It doesn't describe the present or the past. It states a general truth, like "two plus two equals four". Such statements use present tense. The sentence has a major weakness in that it is not clear what is the subject for "don't". Does it say that "people don't" or does it say that "a stranger don't". The second would be grammatically incorrect, so the first is clearly intended. But the sentence will not be heard that way because of the large distance between "people" and "don't". The problem can be corrected by saying "they don't" rather than "don't".

You can make the entire sentece past tense, about a particular event that happened to a stranger, but right now it is speaking in general. The sad thing is that people presumed that the nearby stranger didn't want to converse and didn't start a conversation. Or, it can be about attitudes towards strangers in general in the past: The sad thing is that people presumed that a nearby stranger didn't want to converse and wouldn't start a conversation. So the main factor is 'did' instead of 'does / do.'