Taking that theory to its conclusion, that means that most people are approaching the question of rationality vs. emotion the wrong way by assuming that appeals to reason and logic are the way to convince the average person. Not so; one must convince their emotions first, and then they will reason together a logical framework to fit their emotion.
It's a bit distressing to think about, but unsurprising when one reflects on the course of history that humanity has taken, and is taking.
There's another great bit of research detailed like that detailed in The Elephant In The Brain.
In the 60s and 70s Roger Sperry and Michael Gazzaniga did some research for which Sperry eventually won a Nobel Prize in 1981 where they showed images to patients who had undergone a corpus callostomy where the two halves of the brain can no longer communicate and asked them questions about what they saw. The results were really striking. They did it in such a way that they show the image to only the right side of the brain but then ask the left side of the brain to describe what they saw verbally. They just invent some kind of fantastical rationalization and they seem to fully believe that's what they think despite the fact that it can't be. I'm explaining it kind of badly but that part was jaw dropping. Seems to fit with Haidts research though.
Nothing is jumping out for me personally that I can see, but I know well the feeling of reading all the arguments of one particular school of thought and having this glaringly obvious edge case that no one ever seems to bring up.
Curious to know what those things you see are?
The worst part is it's excruciatingly difficult and extremely unlikely for you to find your own blind spots. So you need to hash things out with other people. As others mentioned the best thing you can do is hold defeasibility and corrigibility as some of your highest values and do your best to understand all the pitfalls in our thinking.