While some of that may be true, it may well be that the solution is to get other's to adopt a morality that has less emphasis on ingroup/loyalty, authority/respect, purity/sanctity

The trouble is, these things are indispensable for any large-scale (and possibly even small-scale) cooperation and coordination between people. Of course, it's possible to masquerade them, but it's always easy to see them in operation among the kinds of people who loudly deny them and insist they're bad. In particular, this certainly holds for the modern intellectual elites, and it's particularly notable in Haidt's own evident (though likely not intentional) bias in the criteria by which he detects expressions of loyalty, authority, and purity/sacredness so as to maximize them on the right side of the political spectrum and minimize them on the left one.

Now, when making this point, it's always tempting to engage in an attack on this blindness and hypocrisy, but at the same time, we are lucky that they exist. An actual disappearance of loyalty, authority, and sanctity in the moral calculus of people would mean literally the end of organized society, so we're certainly much better off if they're negated only in a false and hypocritical way than if they were truly absent.