That's not entirely the case, I think. They have a paradoxical situation: their post-Protestant, post-Humanist sense of moralizing is certainly intact, in that they feel guilty about things like "injustice," or "racism," or "non-inclusivity" when they see them. That is a warped sort of moralizing, and one quite detached from any sort of objective moral grounds; but they certainly have a vestige of moral earnestness, a sharp sense of guilt, and a need to expiate it by way of cruelty to all those they see as "regressive" or "oppressive" in any way.
They've stopped being Protestants, and they've stopped being Humanists, but they've been unable to shake the afflictions of the moral feelings obtained from both. They feel the residual sting of conventional morality; but in their reasoning, they do not think that way. And you can see it in their reactions to moral indictment -- hostility, bitterness, anger, and even viciousness, unchecked by conventional moral duties, but motivated in a visceral way from the residue of the past they are so keen to shake.
It really is, admittedly, a very superficial and confused kind of moralizing they do...which is why I have to term it "moralizing" rather than "morality." It's ungrounded, inconsistent, volatile and visceral, but not informed, rational, calm and genuinely just. They're doing the sorts of actions that suggest moral earnestness, but they have no deep root of any sort of moral reasoning under it. It's from the gut, and driven by some rather questionable motivators, such as guilt, hypocrisy, envy and covetousness...of which they have plenty. (They're all about the envy, for sure.)
But the reason underlying it goes back to people like Foucault, who was really an applier of the Nietzschean postulate, that all moralizing simply is a sham cover for the "will to power." That is, the only actual meaning of moral language is as a strategy for seizing power for one agenda or another. Underneath all the apparent moral earnestness, they have been taught, people are really just selfish and using moral words to advance their own particular purposes of oppressing others. The world is, in truth, a plain upon which "ignorant armies clash by night," to parrot Arnold; and so all one can do is employ one's own moral language as a kind of scourge to drive out the opposition, and to win space for one's own agenda...which, fortunately for them, Marxism instructs them is bound to be a utopia and "on the right side of history."
So for them, moral language gets heard differently. When you say, "X is wrong," what they hear is, "X is against my agenda." And they reply with, "Well X is absolutely right," which they understand to mean, "X happens to fit with my own agenda." It's projection: you're being sneaky, they believe, and so they feel they have a right to be sneaky. You use moral language as a ruse, and so they feel they ought to: after all, as Nietzsche taught us, that's all that's going on anyway, when we strip away the veneer of moralizing. Under everything is a bitter power struggle between competing agendas -- theirs being better, and yours being worse. You hit them with the moral flagellum, and they'll hit you with the moral flagellum. That's how it works, they think.
But nothing they do in service of this worldview makes them feel better. So they viscerally resort to ever more extravagant demonstrations of violence and rebellion, in an effort to quell the fires in their belly of leftover guilt and moral confusion.
Make no mistake: the Left is very involved with morality, and very interested in using moral language...but it's a totally different way of thinking about what we're all doing. Their world is a landscape of dissembling, guilt, hostility, oppression, victimization and competing agendas, in which moral language sits very lightly on the surface...even though a sense of moral guilt burns very deep in their consciences.
This is yet another reason why, for them, oppression and racism and whatnot have to be called "systemic." It means that even when they can't identify any real oppression, they still feel it in their guts. So they explain it away as nebulous "systemic oppression," which can never be located, explained, and especially, remedied. Personal racism can be addressed; "systemic" racism floats away from us and surrounds us like oxygen, and for them, explains why no matter how extreme their gestures of moral earnestness get, their feelings of guilt never seem to go away.