I think it's fairly obvious that intersectionality (i.e. the study of how different identities can combine and cohere to create systems of privilege) is a valid topic, and that e.g. white men are not inherently more deserving of status and resources just because the current system of capitalism prefers them at the moment.
I would actually be okay with intersectionality as you state it here if applied honestly and consistently. For example, almost all of what we call “structural racism” is in fact the intersection of “blackness in American culture” and “urban poverty”. The intersectionalist would recognize that the two interact, but are also independent, and blaming all of the problems of black people on “white supremacy” is going to miss the mark.
Likewise, an honest intersectionalist would note that whiteness and poverty can also interact in such a way as to make, say, generational poverty in West Virginia, really fricking awful.
An honest intersectionalist would note that in certain contexts (e.g. universities) women and minority identities become an advantage.
But instead, to today’s woke, the only ‘sectionalities that matter are race and gender, and ”white and male” can only ever give privilege (privilege that apparently outweighs generational poverty).
The black Princeton grad lecturing an unemployed opioid addict in West Virginia about his white privilege might be woke, but they sure as heck aren’t practicing intersectionality.