Long, but worthwhile
I think there really is something to this. He puts it in terms which will be somewhat inflammatory to self-identified *L*iberals and Progressives, but that doesn't make it incorrect. I have to disagree with his jokes about Democrats/Republicans, because those are just another example of tribalism.
As a person who fits neatly into neither the Conservative or Liberal camp, but self-identifying as conservative and (small "L") libertarian, I see a lot of behaviour that can only be explained by this moral equivalency that he points out. The only way that one could close one's eyes to the obvious fallacy is early indoctrination and identification. This movement plays into out natural human tendency towards tribalism. If you can make people identify with a given group early enough, they will support that group (in the majority of cases, there are always individuals at the margins) over any argument, over any logic, over any truth, because their entire identity is tied up in that group focus, and they are emotionally unready to abandon that identity, because human being are fundamentally social animals. Being outcast from one's tribe is socially and genetically risky.
People who profess this moral equivalency, nonetheless often display behaviour that contradicts it in many ways (revealed preference, in economic terms). They still manage to choose for themselves, usually based upon some measure of self-interest and personal taste, to some degree of efficiency (perhaps more or less impaired by impassioned beliefs in "social justice"), personal standards of behaviour, even as the more diffuse and distant the decision becomes, the more inline with the philosophy of moral equivalence. So they feel outrage when their paycheck is small, but excessive taxation of "the rich" is ok. They are hurt and angry when robbed, but other people who protect themselves should just "give them what they ask for" rather than protecting their lives and property with restrained, ethically and legally justified violence (right to bear arms.)
My self-image is not tied into my politics, I don't automatically think that one's political oreintation makes one more moral. I think it simply makes one wrong or right on given issues. In some cases there are definitely grey areas, where it is difficult to know what is right, but the vast majority of issues can be clearly seent to be black or white, right or wrong, IF one has a philosophical framework in place that allows one to evaluate clearly, to discriminate on the basis of fact, results, and (far distant third) preference, rather than equivocation, self-hatred, and need to identify with an in-group.
I do note explicitly here that Republicans have their prejudices as well, and not all of them are rational. Some of the more fringe religious get on my nerves as well, and just as many people inherit their Republican identity as Democrats, but "Liberals" and "Conservatives", "Republicans" and "Democrats" all tend to look upon themselves as arbiters of morality, rather than simply people trying to find the best policy. Even (big "L") Libertarians refer to themselves as the moral choice: "The party of principle".
People need to get off their moral high-horse, embrace some open-minded empiricism, and give each other space to breathe.