"Never attribute to malice that which can adequately be explained by stupidity."
You've probably heard that one. Here's a corollary:
"Never attribute to stupidity that which can adequately be explained by ignorance."
When you find yourself in a serious disagreement with someone, first give them the facts as you see them. Stick to what you've observed firsthand, not your interpretations or hearsay. You'd be amazed at the people you can find common ground with just by sharing your experiences. Second, if they agree that you saw what you said you saw but they still don't agree with you, silently decide for yourself whether or not they're just dumb. If you think they are a smart person, you may reluctantly conclude that they are malicious.
Now here's the tricky part: do them the favor of turning this procedure around on yourself. Listen to the facts as they see them - carefully restrict them to their own firsthand observations. Give their observations the same weight as your own in your interpretation of events. If after careful consideration of ALL the facts you still disagree with them, then silently decide for yourself whether or not you are just not as smart as they are. If you think you're not dumb, but you can't come to some kind of agreement with them, you might be malicious.
I like to trot this one out during election season, but it never works.