I think this article (as well as another one on the site, The Complex Relationship between Marxism and Wokeness) is among the most perceptive ones I've read dealing with these issues. Particularly I was impressed by his ability to distinguish between what he calls critical justice theory (CJT) and Marxism, rather than go for the usual "aren't these pomo-neomarxist types just so stupid and annoying". He's actually trying to honestly understand how his adversaries think, and seems to do a relatively good job of it too, even though he's a bit flippant at times.

I can't vouch for the accuracy of these articles all the way through, but that he was able to make this distinction certainly works in his favour as far as I'm concerned.

For background, I used to think for a long time that I was Marxist. I do no longer think so, even though letting go of labels doesn't necessarily change one's actual politics too much. And even back in the day I was a Marxist more for what it stood for politically, rather than for all that Frankfurt School and other cultural analysis stuff which always felt too airy-fairy to me (I don't have a university education which might explain a thing or two).

I think I have a lot in common with Lindsay. Classical liberalism and classical Marxism are both in the Enlightenment tradition, and that's what I share with Lindsay against the kind of CJT activism he describes in the article mentioned in the OP. While I think good Marxism is better than good (classical) Liberalism, I also think good Liberalism is better than bad Marxism.

For example, I don't think it's impossible for liberals to admit, in principle, to a "weak standpoint epistemology" where your social position has an effect on what you are likely to know (and you won't be aware of what you don't know). In this view the facts are still out there, even if they're hidden from you because of your biased approach that you're not aware of. Marx's theory of ideology is, by and large, within this tradition when he argues that the bourgeoisie (even though not necessarily all bourgeois individuals) cannot "understand" the labour theory of value for example, because that would undermine their own class position. In contrast the proletariat — a new, rising, and this time really universal class — doesn't have these blinkers on and so can come to realise what's real, unlike the bourgeoisie that is able to stomach only the kind of ideas that don't threaten its power.

The point is that the facts exist, but bourgeois ideology acts as a veil to cover them. For Marx, "analysis of consciousness and ideology is grounded in the belief that mystification is susceptible to being unmasked by knowledge", like Michèle Barrett says (The Politics of Truth. From Marx to Foucalt, p. 9).

Now, I don't know to what extent "weak standpoint theory" is, or can be, part and parcel of Liberalism (I don't know the Liberal tradition well enough). But I don't find it impossible that a Liberal could accept it in principle, at least as it applies to individuals, even though they probably wouldn't accept the "class epistemology" approach that's central to classical Marxism (and I'm not sure to what extent I accept it either. Barrett's book that I mentioned makes a convincing case why it shouldn't be accepted).

However, to the extent that Lindsay's description of CJT is accurate, CJT has let go of this "weak" version of standpoint epistemology and embraced a strong one, where your social position and interests don't obscure the facts (which exist objectively, regardless of your consciousness) but instead constitute them. I think it's credible to claim — like Lindsay does — that this view is Marxian but not Marxist. (Once more I salute him for being able to make this distinction.) It is, because Marxist theory of ideology is a standpoint theory, and CJT is a standpoint theory. (Liberalism in its basic form I believe is not a standpoint theory.) But it isn't, because Marx's views are still inside the Enlightenment tradition (and one could argue, though not without controversy, inside the Humanist tradition as well) where the world is still universally knowable in principle, while CJT is not.

Another thing I would say Liberals don't necessarily have a problem with is a "weak version of social constructionism", meaning that while, for example, someone being a mother is a biological fact, what someone's being a mother means socially cannot be understood in the same way, and the social meaning is socially constructed (i.e. not a simple, given "fact"). But CJT has embraced a strong version of social constructionism, where pharaoh Ramesses II couldn't have died of tuberculosis, because the germ that causes tuberculosis was discovered only in 1882.