But intersectionality doesn't have anything inherent to do with socialism/communism or even Stalin's reign of terror. At its base level all intersectionality is, is a venn diagram. You put all your component variables as circles and the center, the intersection, of all those identifies you.
Where it connects with the Left or socialism or whatever is that they can use it to show that many disadvantaged groups fall together and thus have shared interests at a level above mere traditional Marxist class. And often you can fall into what is their giant venn diagram via your class, gender identity, race, etc. That you aren't any single component, but you share many of them.
It's certainly abused and used stupidly by various groups (like the progressive stack or "oppression olympics" where people try to count up how often they fall in), but what isn't?
It's an old idea, certain religions, women and blacks were allied in the United States in the 18th and 19th Century as they were all oppressed by the system. They had a shared intersectional interest.
I can't say without looking what revived it and tried to outline it as an academic theory, I assume it was in the 1970's in the social sciences mostly because that's where seemingly everything that describes things stupidly comes from.
Mandark will make sure to correct me where I'm wrong as part of his project to make me a better person. Unless he's a coward. (Or anyone else, like many I really looked it up in recent decades when it went semi-mainstream in academia, which was still a few years before it hopped onto Jezebel and elsewhere. I'm sure Mumei posted a few hundred books you could read about it.)