I think "class privilege" is useful because there will always be a class that holds privilege over other classes.

But I don't think "male privilege" or "white privilege" are useful because they presuppose the conclusion. Power can shift. Because men historically were privileged along the axis of sex doesn't mean they always will be (although I'm fairly glum about this one!). Because white people were historically privileged in the US along the axis of race/ethnicity doesn't mean they always will be, and with "white privilege" there is the additional complication of not having a clear, coherent definition of which groups count as "white."

I think privilege as an analytical tool is overbroad. I see it as a way to dodge performing a specific, situational understanding of power dynamics. But those specific, nuanced, thought-through analyses are exactly what we need on the left right now. There's too much use of phrases to short-circuit really looking at and seeing how phenomenon are operating. That's what gets us things like "cis privilege."