Why do I say that the postmodernist species of critical theory that prevails today—critical race theory, queer theory, etc.—pseudo- or faux-leftism? Why is woke not left? Because it’s anti-worker, authoritarian, and illiberal. Denying nature and science, this line of thought/practice is profoundly anti-humanist and anti-science. No Marxist would deny natural history and the utility of science. Moreover, Marxism precludes idealism as an epistemological foundation.
The political right labels this faux-left standpoint “neo-Marxist.” But so do many of those who push CRT and the other crackpot theories. To be sure, much of the Frankfurt School so often targeted by the right is properly designated neo-Marxist (Adorno, Benjamin, Fromm, Horkheimer, Neumann), but Herbert Marcuse’s thought is so far outside Marxism that it cannot be with any integrity properly designated as such, and it is Marcuse who is responsible for what passes for critical theory today—that and the corrupting influence of French existentialism/poststructuralism.
Herbert Marcuse, guru of the New Left
You might stop and ask yourself why, if all this jazz were truly Marxist, corporations have taken up its ideas with gusto, pushing them in HR trainings and in external messaging. Why are corporations funding the activities of so-called neo-Marxist groups like Black Lives Matter? Why is it that that, in the academic rhetoric of intersectionality, social class is rarely mention (and never in terms of itself), with no class analysis, while the working class is fractured along lines of race, ethnicity, religion, sexuality, gender identity, etc.? Why do identitarian politics, with all their abstractions and reifications, not merely stand in place of but negate class politics?
Remember, Marx and Engels told us that life is not determined by consciousness but consciousness determined by life:
“The fact is, therefore, that definite individuals who are productively active in a definite way enter into these definite social and political relations. Empirical observations must in each separate instance bring out empirically, and without any mystification and speculation, the connection of the social and political structure with production. The social structure and the State are continually evolving out of the life-process of definite individuals, but of individuals, not as they may appear in their own or other people’s imagination, but as they really are; i.e., as they are effective, produce materially, and are active under definite material limits, presuppositions and conditions independent of their will.
“The production of ideas, of conceptions, of consciousness, is at first directly interwoven with the material activity and the material intercourse of men, the language of real life. Conceiving, thinking, the mental intercourse of men, appear at this stage as the direct afflux from their material behavior. The same applies to mental production as expressed in the language of the politics, laws, morality, religion, metaphysics of a people. Men are the producers of their conceptions, ideas, etc. —real, active men, as they are conditioned by the definite development of their productive forces and of the intercourse corresponding to these, up to its furthest forms. Consciousness can never be anything else than conscious existence, and the existence of men in their actual lifeprocess. If in all ideology men and their circumstances appear upside down as in a camera obscura, this phenomenon arises just as much from their historical life-process as the inversion of objects on the retina does from their physical life-process.
“It is not consciousness of men that determines their being, but, on the contrary, their social being that determines their consciousness.”
What is being passed off as neo-Marxism today is an iteration of progressivism (woke), a praxis advanced by the corporate state to prevent the development of class consciousness by dividing the proletariat into identity groups, treating abstractions in an essentialist fashion, all rationalized by an ideology masquerading as politics for the powerless. It’s an element in the hegemonic control of the mass identified by Antonio Gramsci in his Prison Notebooks. It is not a species of neo-Marxism.
freedom and reason 
A sentiment that I cannot agree with more – Marxism ends with Marx, a few individuals may be said to have advanced the theory (for me that is Luxembourg, Gramsci and Althusser), but the vast majority of critical theory takes its starting place as the individual or ‘lived experience’.
Identity politics is a right-wing endeavour, as it places the phenomena of capitalism (individual agency) as driving the structure of society (classes). This turns Marxism upside-down, leaving us with a fundamentally flawed ideology. It is no surprise that the state and corporations are happy to promulgate this theory, it leaves the individual atomised and adrift in an ocean of self-interest.