Sure. As a psychologist who has conducted research - and has been deeply interested in the psychological aspects of political views for many decades - I was struck by the very poor quality of the theory and methodology of Haidt's moral foundations theory when I first came across it. Unfortunately, I was not surprised that a weak theory got so much positive attention.
I don't know if you know much about research but perhaps you've heard about the "crisis of replication' in the field of psychology. Psychologists (some 90% of whom tend to be physicalists - materialists, if you like) were horrified when Dr. Daryl Bem found legitimate scientific support for some parapsychological phenomena. So they set out to disprove him.
In the course of their attempts, they realized many of the psych studies they relied on to debunk him could not be replicated (repeated). I think this may be one of the most delicious ironies in the whole history of modern science. There has been irrefutable proof of psi phenomena for over a century and psychologists have said things as extreme as, "I know psi is wrong therefore I don't have to look at the data" (Richard Dawkins said basically the same thing as well).
Ok, here's my favorite Haidt critic. https://behavioralscientist.org/whats-wrong-with-moral-foundations-theory-and-how-to-get-moral-psychology-right/
I was so impressed with his rebuttal I got in touch with him and we had a few excellent email exchanges. His critique of Haidt's approach as ad hoc is spot on. Psychologists - who tend to be almost clueless when it comes to the philosophic foundations of their discipline - so often rely on statistics in order to create a basis for their theories.
If you haven't thought about this before, it may not seem obvious, but the scientific method was. designed for dead, mostly unchanging things. It turns out, for controlling and predicting the behavior of (apparently) dead. matter, it's the best we have.
If you look at the rather poor record of much of medicine as well as the many conflicts in evolutionary biology, you can see it doesn't work as well with living things.
When you come to humans, much of it is at best useless, at worst completely misleading - which is why by the end of my doctoral studies, I gave up on the idea of continuing with research.
There's numerous others (just google "Haidt debuned" or "Haidt + critics) and you'll find an increasing number of excellent criticisms.