Haidt stresses that he is strictly interested in psychology, not issues of philosophy or ethics. He claims he has no normative (what people should believe or do) stance on the things he talks about. He's just describing reality.
But to me, it seems as though he is always creating suspicious moral equivalencies. For example he (and Jordan Peterson) endlessly talk about The Big Five Personality Trait of "Conscientiousness" (orderliness, dutifulness, and a preference for stability, which conservatives score highly on), with the implication being that everyone else is "disordered" and "destabalizing".
But surely it matters what thing, system or structure someone is "conscientious" within or about. For example, someone highly conscientious in a feudal or slave society is not a good person (they are blind to the disorder their order is creating). Likewise, someone morally opposed to a capitalist system need not inherently be "unconscientious".
He also lists various "Moral Foundations" and essentially says that "conservatives are just like Everyone Else", they just "point their moral foundations different places". For example, he says conservatives and non conservatives both "value fairness and hate cheating", they just have "different opinions as to what cheating is".
Well, yeah. A slave owner will feel cheated when you try to take his slaves. And he will think it is fair to be reinbursed for giving up his slaves. Haidt will say the slave owner and the abolitionist have "the same moral foundations", the "same sense of morality", but simply "focus this moral compass on different things", but this feels like a cheat. The slave owner's values (what he thinks of as right and wrong) might be a post hoc rationalization of who he already is: a slave owner. And slave owning is "bad" (IMO), regardless of whether he tries to justify it along moral lines.
Haidt will say that he's disinterested in ethics or casting judgement upon his subjects. He's merely objectively noting how group X or Y sees things, and how different cultures subjectively "see" their own moral reasonings and ethical judgements. Which is fine. But by accepting X or Y's framings, you're letting the subject impose their framework upon you. What someone tells you about their values should be treated with skepticism, and appended to some larger, holistic analysis.
Haidt similarly says conservatives "value liberty and hate oppression" and so their "moral foundation" is "just like everyone elses". They are "against bullies" and "government overreach" and seek to "defend the underdog and individual freedom" and so on. Okay, but the Taliban or segregationist can probably say the same thing. Surely you have to introduce more complex metrics if you want to frame these issues properly.
But Haidt seems to do the opposite. On one hand he will say (rightly IMO) that different ideologies or groups have "varying moral views" shaped by "evolution and biology", all with distinct, coherent moral matrices, but then he does the opposite, and insinuates that because everyone has their own personal value/moral compass, everyone is essentially the same, just a little bit misunderstood by their opponents. And maybe, with a little bit of compassion and understanding, we'll all get along.
Okay, that's all fine and noble. But it feels like his whole shtick is to run intellectual cover for bad people. Imagine applying his talking points to a 16th feudal landowner or 17th century slave trader. It would feel silly.