Another way of stating my position:
We all think the same things. The only variation is the degree to which individuals' thinking is refined. Disagreement is the perception that one's thinking is unique compared to another's when in reality it is merely a more-refined or less-refined version of another's thinking.
Political discourse is a good illustration. As I observe liberals and conservatives angrily arguing over things like the role of government I often find myself thinking that they are all saying the same thing.
Why then do people believe that they disagree with each other? Well, I think disagreement is a perception that a few people create, maintain and exploit for economic and political gain. If pro-life and pro-choice individuals were to see that they really have the same fundamental thinking, a lot of power and money would change hands, if you know what I mean.
Indeed, I have been told by a source that I have every reason to believe is well-informed that the pro-life and pro-choice leaders have a history of secretly meeting in private on friendly terms to look for common ground. I can't furnish any proof of it, but I don't think it is mere hearsay. Anyway, if it is true it shows that so much is staked in the public perception that people fundamentally disagree that people who take sides on the most divisive issues have to hide from the spotlight to work on finding common ground.