Identitarianism (aka identity politics) is a descriptive and prescriptive political framework that emphasizes the interests and perspectives of discrete identity groups. Gay rights, women’s rights, black rights, trans rights, and other similar movements push the interests of those identity groups. Some who operate within the identitarian framework often try to lump class issues into that framework, but I think this is in error.
The fundamental problem with cramming poor people into the identitarian framework is that, unlike every other identity treated in that framework, justice for poor people requires their elimination. The appropriate remedy to racial oppression is not to make everyone white, nor is the appropriate remedy to gender oppression to make everyone male. But the appropriate remedy to the “oppression of the poor” (as identitarians describe it) is to make them no longer poor. Poorness is not an identity to be celebrated or lifted up; it is an identity to be done away with altogether. The oppression of poor people is that they are poor people. The same cannot be said for any other marginalized group.
Additionally, there is no evidence that poor people contemplate themselves as a class anyways. Poorness is not a fixed trait (even if it persists across generations), and in the United States at least, I have seen no evidence to suggest that those with lower incomes identify with one another as a coherent group with coherent unified interests.
I point this out because those who reflexively apply identitarian logic to the issue of class often repeat points about oppression and privilege that make sense for most identities, but not in the class context. For instance, I have had the pleasure of hearing people drone on about how wrong it is to demand evidence, rigorous thought, and research because doing so generally requires levels of education that poor people are not afforded. To the extent that such a criticism is valid (and I am not sure that it is), it totally misidentifies the problem. Intellectual engagement is not classist; preventing whole classes of people from acquiring the skills necessary for it is.
You do not remedy that problem by stopping intellectual engagement; you remedy it by eliminating the barriers that prevent poor people from participating in such engagement. That is, you make them no longer poor, increasing their access to education. This is just one example, but the whole slate of usual identitarian criticisms face similar problems. Fundamentally, it makes very little sense to apply the identitarian framework to identities that you seek to eliminate. And poorness is such an identity.