Even where there is an explanation that these are reformist actions there remains a belief that capitalism is as dependent on a range of oppressions as it is on class structure - so fight them all with equal intensity and we should get a revolution!!
I dunno if that's asserted in the texts you've read, but is it here?
Surely the point made by most libertarian communists would be that interlocking oppressions and socially-imposed hierarchies are used to divide the working class and therefore the task of achieving a unified class struggle intrinsically requires that they be expunged as part of the process — ie. it's all part of the same struggle, rather than being, as implied in your post, separate but equally important/separate and one is less important.
One more to add to the reading list, just found it today and it's useful: https://libcom.org/library/rethinking-class-recomposition-counterpower
The mentions of 'privilege' and 'intersectionality' are quite superficial (doesn't address the history and differing usages of the terms, you can see this as a reflection of superficial usage by proponents or not).
The discussion about class is a lot more in-depth, class composition/decomposition/recomposition, class as process vs. category, as well as the definition of class struggle. Author appears to be a WSM member. Takes a similar approach to some of the Viewpoint articles on this, but written in 2013.