In some circles, it goes without saying that Marxism (or, at least, Classical Marxism, or first generation Marxism or whatever) is "class reductionist". I think it's worth spending a moment just trying to get clear on what the charge is supposed to be. To be sure, I think some version of it applies to some (not all) figures on the Marxist Left. I don't mean to suggest that the charge is inherently frivolous or misguided. Still, in my experience, the objection is thrown around so loosely that it's often not clear exactly what's being said. For this reason I've taken to simply asking those pushing the objection to explain what it means before trying to defend Marxism from the charge.
One gloss on "class reductionism" goes as follows. It is the mistake of reducing all forms of oppression, e.g. racism, to economic inequalities. I've encountered some who seem to think that this means that Marxists understand racial oppression to boil down to income inequality or stratification. I've encountered others who claim that Marxists conflate race with "socio-economic status". (Aside: I despise the term "socio-economic status". People seem to say it instead of class because it sounds more technical and "official". But it's a conceptual mess that obscures more than it clarifies. I really wish people would just say "class", even if they misuse the concept. If nothing else, it rolls of the tongue much more effortlessly.)
Others would say that "class reductionism" isn't a view about what explains what. It is, rather, a normative mistake that ascribes unequal importance or significance to, say, racism and class disparities. On this view, class reductionists just don't think that racism is as important as class to study or fight against.
For others, "class reductionist" is tantamount to a strong kind of eliminativism. This version of "class reductionism" holds that because talk of race and gender oppression can be reduced to talk of income inequality, it follows that talk of race and gender should be eliminated in favor of a political lexicon that is entirely based around the concepts of income inequality, stratification, etc. Some eliminativists even claim that there is something wrong with talk about race and gender, viz. that it obscures the real heart of the matter: income inequality. This seems to be the position of Walter Benn-Michaels, aptly dubbed the "Glenn Beck of the contrarian left" by Richard Seymour. This is basically a version of the familiar racist ideology of colorblindness, albeit with a generally left flavor.
If Marxism were class reductionist in any of the above senses, I too would reject it. But it's not clear that Marxism makes any of these claims. The normative mistake has been made by Marxist as well as non-Marxist socialists, to be sure. And they should be ruthlessly criticized for having made the mistake. As Trotsky argued, the "mistake" is usually connected to latent racism among some in the working class movement. Trotsky said of this phenomenon that "the argument that the slogan for self-determination leads away from the class point of view is an adaptation of the ideology of the white workers". "The Negro", Trotsky argued in 1939, "can be won to the class point of view only when the white worker is educated", i.e. only when white workers are disabused of racist beliefs, when racism is smashed within the labor movement. I don't think the normative mistake is a feature of Marxism as such, in fact, I would argue, Marxism speaks against abstractly and inflexibly ascribing unequal significance to race and class. As a form of analysis that looks at concrete conjunctures as dialectical totalities, Marxism is attuned to the combined and uneven development of economic and political formations. This is what underlies some of the best Marxist scholarship, e.g. on questions of the transition from feudalism to capitalism, on colonialism and imperialism, on national liberation struggles, permanent revolution, etc.
Moreover, Marxism makes no claims to the effect that racial oppression boils down to differences in income or "socio-economic status". First off, Marxism does not trade in concepts such as "stratification" or "socio-economic status" at all. Marxism offers a very rigorous, relational definition of class that differs in many respects from the ordinary language use of the term in everyday speech. The basic Marxist complaint against liberal income-based approaches to inequality is that they wrongly take income inequalities to be sui generis. They don't explain what it is about our economic system that produces income inequalities. Marxism, on the other hand, sees income disparities as deriving from more fundamental asymmetrical relations of power that are rooted in the material conditions of modern societies.
It is a fact that the material conditions of the U.S. social order, from the very beginning, have been structured by racial oppression, just as it is a fact that racial oppression itself grew out of a set of material conditions. U.S. capitalism literally comes into being, dripping from every pore, covered in blood and dirt. Let's not forget that capitalism comes of age in the context of expropriations of indigenous populations, colonial extraction of natural resources, and the enslavement of human beings -in short, what Marx called "primitive (or primary) accumulation". Modern racism emerges out of European colonial expansion and the slave trade. It grows out of a need to justify the enslavement, domination and subordination of non-white peoples to needs of the ruling classes of Europe. Thus, racism and capitalism co-originated in a complex dialectic of mutual development. Racial oppression has been a basic feature of the functioning of the system since its inception. It would be foolish to think that racism could simply fade away without being decisively uprooted by struggle against its historical and material bedrock. It should be clear that no Marxist worth her salt could, on the basis of the analysis above, endorse an eliminativist position.
So, for Marxists, disparities in income, job and educational opportunities, etc. are explained by an critical analysis of the material conditions of social life. What a historical materialist analysis of the system reveals, however, isn't just that racism is a basic feature of basic structure of society. It also reveals that capitalism, as a mode of production, is shot through with contradictions. One contradiction is that the interests of the two most important classes in capitalist societies, workers and capitalists, are diametrically opposed. If workers want a shorter work day, better pay, safer conditions, more voice in the workplace, capitalists want the opposite. But, the clash between workers and capitalists isn't a fair fight. Capitalists have a lot of advantages on their side: a legal system meant to service their needs and stop workers from organizing, a repressive state apparatus ready to defend their interests in moments of conflict (e.g. by breaking strikes), a political system beholden to their interests, etc. We could go on. What this reveals is that class relations, such as the relation between workers and capitalists, are asymmetrical relations of power. The fundamental problem, then, isn't that capitalists enjoy higher levels of consumption than workers. It's not that capitalists possess more stuff than workers that, at the end of the day, is the fundamental problem with capitalist social relations. It's what the capitalists can do to others with the stuff they possess that matters. In other words, Marxists don't fundamentally worry themselves with looking into whether abstract individuals, off in their own corners, are consuming unequal amounts of stuff. Marxists are concerned with social relationships, rooted in the material conditions of capitalist societies, that exhibit exploitation, oppression or domination.
Is Marxism, then, in any sense "class reductionist"? Not if we go by the senses of "class reductionist" examined earlier.
Still, I can imagine further charges of class reductionism that could be leveled at Marxism here. Someone could argue that Marxists are reductionist insofar as they don't understand racial oppression (or any other form of oppression) to be particular particulars, sui generis and completely autonomous from one another. The charge clearly sticks; Marxists indeed do not think that racism, for example, is totally sui generis. Marxism holds that no single part of the social life can be fully understood when torn apart from other features about modern societies and history. Marxists view society as a totality with complex dialectically mediated interconnections between various parts. But does that make one reductionist? I don't see that it does.
Marxists, on the basis of a concrete, materialist analysis of historical development, will argue that we can't understand modern racism without seeing how and why it emerges when and where it does. We don't fully grasp modern racism without learning about European colonialism, imperialism, and the battles for economic/political dominance between the ruling elites of different European empires. Does that mean that racism is reducible to its historical origins? Hardly. Here Marxists must emphasize that ours is a dialectical social theory. That means that racism and class exploitation develop such that there is causal interaction going both ways; the two reciprocally interact, co-evolve, inflect one another, in a dance of mutual reinforcement and tension (one sometimes pulling more strongly against the other and vice versa). Reduction of one to the other elides the dialectical structure of Marxism as a tool for social analysis.
This isn't idle academic squabbling. Getting clear on how forms of oppression are rooted in the system, and therefore bound up with other forms of oppression, is of immense practical significance. This insight underlies the political tactics and strategies of the Marxist left. Most importantly, it shows that an anti-racism that fails to uncover the ways that capitalism reinforces, exacerbates and consolidates racial oppression is doomed to failure. It also shows that an anti-capitalism that doesn't grasp the racial domination written to the very infrastructure of the U.S. economic system is similarly doomed to failure and defeat.