Setting aside the fact that this is a generalization and thus naturally overstating things, I don't doubt that there's some truth to this.

There's a sort of rigidly intolerant moralizing that arose on the internet over the last decade or so, most exemplified by Tumblr, and gen z was right in the middle of it.

It puts me in mind of the Victorian era, with a group of people who absolutely and unequivocally condemn anyone and everyone who violates their rigid sense of propriety, or more precisely, the stereotypes that they substitute for those people. Of course, the biggest difference is that they have a completely different set of rules to which they insist that all submit - instead of a religious morality mostly concerned with sex they have a secular morality mostly concerned with social behavior. But they share that absolutism - the smug certainty that their way is the only way and that any who believe otherwise are not only wrong, but due to the fact that they believe otherwise, so monstrous as to be unfit to even judge.

That last is the trap - the thing that sets that extreme of moralizing apart and keeps it going when it takes hold. Those who come to believe in it end up believing not simply that they're right, but that believing as they do is the defining trait of people who are fit to judge the matter, so they then can and do reject any and all differing views out of hand on the basis that the mere act of holding a different view means that one is obviously an inferior being, and since one is an inferior being, whatever one believes is and can only be wrong. It becomes a closed loop, in which people aren't even capable of considering different viewpoints.

And that's presumably the quality that's being characterized, and with some accuracy, as them not having the skills to disagree.

I'd note though that this is just one manifestation of the problem. It's a new version of it, made possible by social media, and it appears to be notably widespread, and particularly in a relatively narrow age group, but the dynamic itself is likely as old as human civilization.