Absolutely. Both privilege and oppression are real and worth understanding, and at an academic level, intersectional feminism has done a lot of good work in this regard.
Recognising that structures of oppression with regards to race, gender, sexuality, etc. are not totally uncorrelated, but have commonalities that are worth identifying and studying in their own right, is a significant innovation of intersectional feminism, and I respect it.
Similarly, the concept of "privilege" is very worth unpacking. To those who can think of themselves as "just a person" living on some kind of neutral substrate, that feels like the most ordinary and natural thing in the world -- but it's a huge privilege. If you're a woman, this fact is continually thrown in your face, in a way that distinctly qualifies and limits your "personhood". If you're a gay black woman, then the qualifications and limitations genuinely get multiplied. I think it's important to unpack and understand this, and I welcome philosophies that aid in doing so.
(As an aside, I don't consider this kind of cultural analysis is at odds with rationality, until it crosses the threshold of insisting that it is describing the whole of reality in a totalising way, at which point it does start having genuine philosophical problems.)
The problem is that the populist expression of this pretty much boils down to "you have privilege, so shut up", which A.) is illiterate, because "privilege" is neither a personal nor even a cultural failing -- it's the lack of privilege that's a problem, and B.) utterly inimical to fostering any kind of understanding.
Anyhow, I suppose this is no different from what happens when any other nuanced philosophy gets used as a tool in populist conflicts. I have huge respect Buddhism as a philosophy, but it is nonetheless being used as a justification for persecution and genocide in Burma. Here or there, I think it's important to not let enlightened ideas be used as an excuse for being a jerk. (Nor to let jerks discredit enlightened ideas, although on the whole I'm less concerned about this).