first of all, what you describe is socialism which Karl Marx deemed was a step towards communism. communism is a utopian ideal where everything is shared, which can only be achieved in a world free of scarcity. Karl Marx's communism does not have a government once the revolution is complete. Karl Marx's communism is also completely doomed to fail because scarcity will always exist, as well as human nature.

Karl Marx was a privileged trust fund baby with a laughably terrible grasp of economics who thought he could solve the world's problems. his religion is only tangentially related to his shit idea. Most Jews would be insulted to be associated with his ideas.

the Frankfort school was indeed a Jewish school, run by a very small number of Jews that were likely part of the same sect. whether the school was operating honestly or was part of some conspiracy to destroy the West is up for debate in my opinion, but I can tell you everyday rank and file Jews not only know very little about that school, but would actively distance themselves from it given the degenerate ideas that have come out of it.