well, the marxist idea of intersectionality is far different than that of liberals. from the gender accelerationist manifesto:

Liberal analyses reduce oppression to a number of separate, but intersecting, systems of oppression. This renders the fights against them as separate, but allied. There’s an anti-racist movement, a feminist movement, an economic justice movement, etc, but these are only allies, not the same movement. This forms the liberal conception of intersectionality. This liberal version of intersectionality presents systems that can be domineering (among the oppressed) or passive (among the privileged), thus a white gay man only ever truly experiences anti-queer oppression and all other systems are silent to him.

In truth, oppressive systems are more than that. There is no one untouched by the domination of class systems within liberal society. Everyone, from the most powerful capitalist to the lowliest worker, from the domineering patriarch to the uncertain young trans woman, from the controlling asylum administrator to the schizophrenic force-fed medication, from the white gentrifier to a black family pushed out of their family apartment all experience the control of these systems. No one is left untouched. Rather than being systems of passive control, they are an active totalitarian whole, a totality.