whose marxism?

I was hoping either through this post or in class today to sort of "sift out" what Cloud v. Greene's ideas of Marxism are, how they function rhetorically, and in what ways they can be used by critics. It was pretty obvious through the readings that Greene and Cloud diverge at points, but I found Greene's (2006) claim that Cloud, Aune and Macek use "Marxist criticism (that) dialectically reverses the moral reasoning of the bourgeoisie—the universal substitution of its interest for everyone’s interest. As such, the class struggle instituted on a foundation of moral fundamentalism and a politics envious of the state’s monopoly of violence; it is a foundation more likely to bring forward a ravenous hydra from Marxism’s past." I agreed with his point against Cloud but also was left wondering in what ways does even Greene interpret/deploy marxism for his own work and are these particular uses problematic due to their theoretical/methodological inconsistency?