I’ve posted a bit about this before but I’ll rehash for clarity’s sake. To respond to your point, two of the most prominent postmarxists, Zizek and Negri, make the sort of claim you’re maybe implying, that materialism shapes intersectionality in such a way that class remains the central/primary contradiction. As well, all the people who cling to fairly orthodox Marxism hold to the idea that class is somehow privileged (Jameson, Harvey, Monthly Review types, and all the various Trot, post-Stalinist and Maoist parties in principle).
After people like Lacan, Foucault, Deleuze and Derrida (under the heading “poststructuralism” in America) were on the scene, it became impossible for most continental philosophers to hold to the privileging of economic/material class struggle and the necessity of proletarian achievement of communism. This is because of the (various forms of) poststructuralist views of subject formation.
In classical Marxism, the political subject is constructed by a simple relationship to the means of production. The story: If you are “doubly free” – free from ownership of the means of production and free to sell yourself on the market – then you are a proletarian. If you own capital, you are bourgeois. Nothing can interrupt this basic logic, which plays out over time where the proletarians become a majority within capitalist society and then straightforwardly take power in some sort of revolution and institute socialism.
Now, it became obvious pretty quickly that something was wrong with this picture, since proletarians weren’t all conscious of their position as proletarians, and they weren’t acting in an obviously pro-communist way all the time. So first Lukacs came along and said well yes but they are everywhere confused by capitalist propaganda and, more importantly, the system of price signals and such, that depend on selfishness and hoarding and such. And that sort of helped build the model of “false consciousness” which most Frankfurt School types supported and such. The idea in this model is that, yes, proletarians ought to act a certain way if they are aware of it (every proletarian is a good communist in theory) but unfortunately they get a bit confused at times.
What Gramsci did, soon after Lukacs, was say, well, yes, classes determine history, and eventually proletarians will defeat the bourgeoisie, but things are a bit uneven within broad social categories. So people are at various stages of development/consciousness and there are a lot of varied types of social positions in class society. Capitalism survives in the West because the bourgeois institutions create cultural hegemony, which is the manufacture of consent through control of people’s ideas about themselves and so on. Revolution, therefore, needs to be counter-hegemonic, fighting a war of position against the prevailing ideology. When Stalinism collapsed, most Western Communist parties adopted this position as their own as a cover for parliamentarism: They said they had to build a democratic majority to win over power.
However, for Laclau and Mouffe, the Gramscian position still says that if you are a proletarian in the sense of a member of the industrial working class then you are necessarily a proletarian in the sense of pro-communist. They argue that poststructuralist critiques of subject formation mean that Gramsci has to be taken in a way that the political is entirely autonomous of any sort of base-superstructure formation. That is, just because you are a “proletarian” in the Marxist sense doesn’t mean you necessarily come with any fixed view of yourself or political project. Moreover, there are many facets to your identity, which you need to negotiate yourself. What the “right” position happens to be is a matter for your own deliberation. For Laclau and Mouffe, this is the only way to understand the rise of the new social movements, such as feminism, anti-racism and environmentalism. For Laclau and Mouffe, then, any given structural position only becomes a particular subject position through a process of negotiation and antagonism.
Why Zizek became famous is largely because he attempted to rebut this position of Laclau and Mouffe’s. Of course, he understands the material at such a level that he knows he can’t simply assert that class is privileged in the old way – he knows you can’t go back there. So what he suggests is that class is repeated in a Hegelian sense as the truth that underlies other oppressions. The idea is that, yes, identity and therefore associated struggles are intersectional, of course, but class plays a suturing role in establishing and maintaining other oppressions. Moreover, these other oppressions are always in terms of a sort of “class” in themselves – race is about racial hierarchies, and it also about race-related socio-economic inequalities.
A closely related issue is that Laclau and Mouffe say (following Lacan) that their viewpoint is rooted in a certain social imaginary which is prevalent in the societies they live in, since they are saying they are situated in history, they aren’t coming up with this out of thin air. And they say this imaginary is radical democratic pluralism, which is teasing out the radical conclusions of the liberal-democratic impulses of liberty and equality, which they see as foundational to the Western radical tradition. Well, Zizek says, why not position yourself in the global radical tradition which has the imaginary of class struggle. Combined with class as a suturing role within society, this entirely transforms the question of the state! On one side, Laclau and Mouffe are forced to defend liberal-democratic institutions as an adequate starting point to something better, and on the other you have Zizek suggesting that liberal-democracy needs to be questioned at its core, that the state be seen as contingent, and that “illegal” excesses of the lower classes need to accepted as central to radical politics.
Negri (with Hardt), for his part, does something similar, although from Deleuzean and not Lacanian angles. He says that “the proletariat” doesn’t make sense as a social category in post-Fordist service economy centered on immaterial labour. So he develops the concept of “the multitude” which he sees as containing all the contradictions of different subject-positions, but within a sort of unity as a class concept. The multitude exists insofar it is oppressed, and it reacts against this oppression. Negri leans on Foucault for a concept of biopolitical production which suggests that life is regimented and regulated itself in contemporary capitalism, not just commodity production. So, for example, for Negri the artist who raises the value of a poor neighbourhood through gentrification that is captured by a land developer is producing value that is being extracted from the commons in a certain sense, and in that sense they are part of the multitude. Since immaterial production relates to almost everything, then, this is how class subsumes other oppressions too, and helps explain the rise of feminism and so on (since women are part of the social factory when they produce at home and so on). And so Negri is excited about OWS and such because he sees it as an explosion of new forms of democracy of the multitude.
So that’s my tour of contemporary intersectionality versus class among postmarxists I guess. I personally am critical of the recuperation effort by Marxists to try to “save” the privileging of class struggle, and I frankly think that most books sold by these types are probably to people who just want to hear that their old beliefs in Marx are being shored up. But, as I said, I tend to think that socialism is really important for a lot of reasons, so I worry about subordinating it to liberal-democratic institutions. On one hand, accepting liberal-democratic institutions gives you all the resources of liberalism. On the other, accepting the more class-centered revolutionary tradition gives you all the resources of Marxist revolutions.