The basic premise of "The Righteous Mind" is that liberals, conservatives and libertarians use different moral metrics to judge the veracity and fitness of political candidates and of their world views in general. Their outrage or praise at statements that politicians make depends on how well or badly these statements score on their spectrum of moral values. Haidt's point is that most of the disagreement on political issues between liberals and conservatives boils down to a subset of six moral 'foundations' that they score politics on.
The six moral foundations are: care/harm, liberty/oppression, fairness/cheating, loyalty/betrayal, authority/subversion and sanctity/purity. Based on several studies conducted by him and his colleagues, Haidt has concluded that in general, liberals value the first three values disproportionately while conservatives value all six values equally. Thus as an example, liberals get very worked up about the oppression of minorities because it scores very badly on the "care/harm" and "liberty/oppression" metrics, while religious conservatives get very worked up by LGBT rights because it scores very badly on their "sanctity/degradation" and "liberty/oppression" metrics. Libertarians view the liberty/oppression axis as being as overwhelmingly important.
The following chart neatly illustrates these differences:
Haidt also refers to these moral foundations as sacred values, considering how intensely liberals and conservatives often cling to them. Seen through this lens of sacred values, it's very interesting to look at the Giant Conflagration of 2016 (otherwise known as the 2016 US election). When Trump said all those obnoxious things about Hispanics or women or Muslims, he scored very low on liberals' main moral values (the three on the left): by insulting certain racial or demographic groups, he was showing that he did not care about them, he was purportedly infringing on their liberties and he was also not being fair to them. As the chart shows, concern for the care and liberties of victims of oppression is liberals' most sacred value, although it is also valued highly by conservatives. Minorities and women are often thought to fall in this category, and so the violation of this value disqualified Trump in the eyes of liberals right away.
What they failed to realize was that he was still scoring very high on the three conservative values on the right. Many conservatives who supported him disavowed his words, but that wasn't why they would have a big problem supporting him. He was clearly showing loyalty to disgruntled working class whites, he was being an authority figure to them, and in some sense he also seemed to be preserving the sanctity of their way of life. It's not that conservatives didn't care about the left three values, it's just that all the supposedly disqualifying things he said still made him score very high on the values on the right. On balance he thus still scored favorable.
The mistake liberals made was in thinking that his words would be as important to conservatives as they were to them, but because those words didn't really affect the three major values on the right that conservatives found important, they didn't matter much to them. It's a good case of missing the forest for the trees, and hopefully liberals won't make the same mistake next time. All six foundations are important, however, so liberals cannot be faulted for being angry at Trump's shoddy treatment of the three on the left; as Haidt says, even conservatives value these foundations.
The next four years are going to be a giant experiment in testing all these moral foundations. If the worst that everyone thinks about Trump comes to pass, this country will be in bad shape. That would be because he would have failed on all six foundations: for instance, if he does not deliver on promises to bring jobs to the white working class, the moral foundation of betrayal/loyalty and authority/subversion which they have largely staked their support for him on would take a potentially existential hit. He would have then failed both liberals and conservatives. If on the other hand, he manages to actually follow up on the positive promises that he has made, especially regarding job creation, and also manages not to significantly hurt the other moral foundations on the chart, who knows, perhaps everybody would have been wrong about him after all. For now the best strategy is the one recommended by the Zen Master: "We'll see".