So consider an alternative claim: instead of “Progressives spend significant time ordering the oppression pyramid,” the claim becomes, “In some instances, especially among college-age leftists, some assholes will silence other people by claiming that, as a member of a relatively privileged group, another leftist shouldn’t have a voice in a particular discussion, and should be humiliated for speaking up.”
The first claim reads like patent nonsense to me. The second claim is definitely something I’ve seen on multiple occasions, and I hate it and argue against it when I see it. And when I speak against it, I generally have company, including other people on the left, including people from relatively oppressed groups.