One of the keystones of Jonathan Haidt’s work is the fact that conservatives usually understand liberal arguments, but liberals don’t understand conservatives. From it he builds the theory that conservatives operate with all six of his moral foundations (harm, fairness, liberty, loyalty, authority, and purity), while liberals only strongly possess the first three.

This theory is nonsense, as anyone who has spent any time around the left should know. (Ironically, Haidt considers himself a liberal). Conservatives understand liberal arguments because we live in a liberal culture. Liberal argument is hegemonic. Are native Spanish-speakers in the US more likely to understand English than native English speakers in the US are to understand Spanish? Yes? Just so.

In fact, liberals espouse loyalty to liberal institutions and causes, obedience to liberal heroes and leaders, and are as concerned with liberal purity. The evidence is there, if you ask the right questions. A Mormon liberal is not likely to be tolerant and forgiving of someone who blasphemed Kate Kelly, betrayed dissenters to the Church, or taints their home with patriarchal material.

Haidt mostly didn’t ask the right questions. He focused on conservative spectrum loyalties, purities, and authorities.
Why didn’t Haidt ask the right questions? Well, one explanation is that Haidt himself is a liberal. One of the principle dogmas of liberalism is that it doesn’t have loyalties, authorities, and purities. Much of liberalism is invisible to itself.

The difference between conservatives and liberals is not that only conservatives obey authority, insist on loyalty, and reach for purity. Everybody does that. It’s human. The difference is that only conservatives are aware that they are doing it.
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No man can serve two masters.
Satan’s greatest lie is that he doesn’t exist.

Update: To be fair to Haidt, there is a wrinkle on why he missed liberalism’s additional moral foundations that does him credit. Haidt wants to diminish red-blu partisanship, so he likes the idea that liberals and conservatives differ merely by the addition of some extra moral foundations. That means that a lot of their rancor comes from misunderstanding and can in theory be cleared up.