>Intersectionality is supposed to be a framework of understanding power amongst different groups but often gets applied to an individual basis which is ironically a very much against a sociological way of thinking.

Marx subscribed to this way of seeing individuals as mouthpieces for the collective. So did people like Marcuse. You know, one of the influential thinkers from "Critical Theory of the Frankfurt School of Marxism". Name sound familiar? You are giving these people more credit then they deserve.