Spicy question maybe, but I'm interested in your takes.
Personally, I think there's some major issues with at least the terminology of the 2 phase model of lower/higher stage communism or socialism/communism as the terms are used in classical theory. Specifically the 'lower stage' or 'socialism' term is problematic.
In the age of revision and after the success of counterrevolution it has become clear that there is in fact a transitional phase leading up to the classical transitional phase. Societies did not jump from developed capitalism to socialism immediately and even the states that arguably did were forced to roll back some of the core tenets of 'socialism' as it is described in Marx, Engels and Lenin. Namely no private ownership of the means of production and no exploitation of man by man.
To ultras this just means countries following this path aren't socialist. So then China isn't, Cuba isn't, no country still is really and those of us claiming they are then have to be revisionists. And to be fair, if you're dogmatic you can make that point going from the source material. China itself recognizes this inconsistency, thus not seeing itself at the stage of socialism. Yet it's a socialist state. But then what do we actually mean by 'socialism' when we use the term like this? Just a dictatorship of the proletariat? Any country in the process of building socialism?
That question comes up all the time and confuses the fuck out of people, because the term is either not applied consistently or as it's defined is lacking. I think discourse in the communist movement and about AES would profit immensely if we had a more consistent definition or usage of the term or a better defined concept of what that transition to socialism is and how we should call it.
Intersectionality itself may not be explicitly materialist, the theory which supports it (which was done so through a marxist perspective) is standpoint theory which is completely materialist. The tokenization and other aspects occur in practice, which is unfortunate but not what the theory itself advocates.
To boil it down, do physical bodies which have a continuity in time and space have aspects or characteristics which are evident as a result of their environment and the effect of the environment on it?
In geology an example would be stratification. A large vertical column of earth has within it a novel set of characteristics corresponding to the effect of the environment around it. For example different geological epochs which can be determined through radiometric dating. Another could be a layer of a specific type of soot from the blast of a nearby volcano with compounds novel to the composition of the volcano. This continuous physical body is has information which is evident externally by observers or by other physical forces.
Similarly the person with an intersection has specific knowledge by virtue of themselves having experienced it. This may not be available to them readily, it may not manifest physically either. Perhaps even outside observers do not know and cannot know. None of that means it did not happen and was not potentially causally involved in the sequence or set of events they experienced.
EDIT: To add to what you said about 'whack-a-mole', it always seemed to me the general distaste towards some of the methods of intersectionality were founded in the relativism individuals engage in. I agree in this sense it becomes 'whack-a-mole' as what is kept at the forefront of individuals is their own material conditions and experiences to the consequence of others. Each intersection here becomes a unique identifier which is atomic and incommensurable which does not lead to productive engagement. I think the rational comes after the material conditions they face. However, I don't think it is appropriate to shoot the messenger for the message, or rather the framework for consequences as a result of it being used by certain individuals in a certain space who are known to take advantage of whatever they can to gain whatever slight they may over others.
If these individuals had a better context with which to engage (e.g. Marxism, or any other developed school of thought) then I don't believe the relativism nor the 'whack-a-mole' would be anywhere near as prominent. The breadth of human experiences and intricacies needs to still be dealt with, and in this case I think it acts as a bolster to Marxist-Leninism which is rather vague initially about how it organizes people.
Thanks for the detailed and thought-out response, I really appreciate it. My frustrations come purely from the mainstream application of intersectionality which decontextualizes everything for the sake of primacy of racial and social hierarchy, completely ignoring the basic question of why these hierarchies even exist in the first place (presumably because of typical western orthodoxy of "human nature"). I have definitely been rethinking it and seeing its value even in Marxist applications.