basically, they aren't actually marxists in any meaningful way. the philosopher they actually follow is foucault (sort of.), who may have claimed some affinity with marx but was actually largely seen by most of the left as a dangerous reactionary. i would put myself more in the tradition of chomsky, who famously did not get along well with foucault. most of the criticisms you see of the sjws are foreshadowed in the foucault-chomsky debate, which was itself a small manifestation of a set of bigger epistemological problems about things like the value of empiricism and the value of theory.
the way we get foucault's ideas nowadays are not direct but through a synthesis with the historical progressive movement in the united states, which was always largely a socially conservative movement. this was the movement that brought us prohibition, for example. it spent much of it's time railing against the godlessness of liberalism. while it made some positive contributions, those contributions came in the form of christian goodwill rather than in the form of any kind of legitimate left-wing ideas. it had no meaningful concept of class.
but, that was the value of synthesizing it with foucault. unfortunately, however, when you take foucault's theory of power and you combine it with christian progressivism, what you get is something very similar to burkean conservatism - that is, toryism. you have to remember that foucault was writing from france, where the narrative was still very much rooted in the french revolution and debates between rousseau and burke. what foucault basically did was that he converted burke's idea of proper class hierarchy into a system of control to fight against; foucault was somewhat of a vulgar burkean. but, when the christian progressivists (who were already burkeans at heart) picked that up, they missed the vulgarity of it and largely just picked it up at face value.
so, this idea that sjws are leftists or marxists is completely wrong. what they are is puritans, conservatives, tories, burkeans. my criticisms of them and what they want follow from the left. they are a combination of the criticisms of chomsky against foucault (or against zizek), the criticisms of bakunin against marx and sometimes (unfortunately) are even the criticisms of rousseau (or paine) against burke.
https://www.youtube.com/watch?v=OzrHwDOlTt8
https://www.youtube.com/watch?v=s_c3cNG5ttk