I would agree with this, except I have heard a more useful phrasing “deference hierarchy” or “deference politics”. There are unwritten (but quite obvious) rules about who should yield to whom in any given discussion. People declare their position by preceding their statements with “as an XYZ…” and if someone speaks out of turn, you will quickly see the contours emerge. In that lens, intersectionality becomes a reminder that intersecting identities have rank, i.e. a white person can’t claim priority just by being a woman or queer, because that’s not enough intersection.
The above description might seem hostile because it’s supposed to be observed but not mentioned. You’re certainly not supposed to describe in reductively provincial terms like a pecking order, nor to openly admit that some voices get precedence for reasons other than merit of ideas. But IMO, while at times it does get ovewrought, it’s a valid thing that mostly shouldn’t cause a lot of heartburn. More-oppressed identities ought to get more precedence over any other individual voice, and should have proportionally greater sway over the collective voice.
It’s proper that it exists and therefore silly to pretend it doesn’t. The demonization comes from cishet whites (mainly men) who are distressed at the knowledge that there’s one social hierarchy that we can’t dominate.