There's certainly a lot to learn from Haidt and from cognitive science in general. But I think it's crucial to distinguish conservative rhetoric from the systematic effects of their policies. I don't know how solid Haidt's research is in coming up with the so-called conservative values in his model of morality. I do know there's a crisis of replication in social psychology, so I wouldn't bet the farm on that research.

As far as I can tell, it turns out that regardless of how conservatives and centrists rationalize their behaviour and pretend there's such a thing as "conservative thought," the social order that follows from the policies conservatives fight for aligns with social Darwinism and with a preference for dominance hierarchies. So regardless of the propaganda and conscious aims, conservativism is effectively a throwback to animality.

Haidt's moral theory obscures that unsettling fact. I'd be suspicious of that theory, though, because he seems to have bowed to political pressure from conservatives and libertarians in adding liberty as a separate value, and of course he's against "social justice" as an expression of postmodern progressivism on American college campuses. So regardless of his personal politics, he's cashed in by defending conservatism in the American culture war. (I'm also opposed to wokester extremism, but likely for different reasons.)

His model makes it seem as though conservatives are more balanced than liberals. But being more grounded in animal instincts isn't necessarily a moral advantage, since animality is servitude to nature's amoral forces. So-called liberalism (i.e. humanism) is a promethean revolt against nature. That anti-natural creativity is the birth of true morality.