If I were to try to provide a specific diagnosis of the problem, I think it is that people tend to improperly conflate things.

Quite often - far too often - people will perceive one claim as being inseverable from a broader genre of claims or group of people, when in fact they are entirely independent from each other.

For example, if I said I think the idea, attributed in the Bible to Jesus, that we should "turn the other cheek" to our enemies has a lot of merit, some people might claim that my endorsement of that idea is an implicit endorsement of the whole Bible, or of Christianity in general, including the Christian Right.

But that's entirely absurd. "Turning the other cheek" is all about showing your enemies that they can't hurt you, and there are any number of reasons to adopt it as a life strategy, even if you believe the rest of the Bible is rubbish, and that Christianity is a pox on the world.

One solution to this problem, I think, is basically to take every conversation one idea at a time. And the other solution is to talk more about ideas, and less about people. Because ultimately, the value of an idea doesn't derive from who said it, but by whether it makes sense on its own right.