The illiberal left "believes science is real" while the illiberal right maintains "facts don't care about feelings". They both want to lay claim to truth because of the power you gain when you're seen to be in alignment with truth. Very postmodern of them!

The illiberal left is perfectly happy to ban content too, just like the illiberal right; they just have different criteria ("hateful" vs. "corrupting").

The group identity vs. personality cult distinction seems to be holding for now.

But the illiberal left is increasingly content to simply flat-out lie--they just have a slightly different cover than the illiberal right. (For instance, maybe the cover is "speaking my truth" which, when it's about a matter of objective reality, is really indistinguishable from having "alternative facts".)

I think they're growing less and less distinguishable in methods, and primarily differ in content: who gets the power, and what does that power look like.