AFAIK actual commies never used gender or ethnic quotas and were opposed to feminism and other identity politics.
In politics left and right is pretty corrupted and meaningless. In fact people can and do believe what they want to believe and justify to themselves that they hold the superior position.
Everything is mixed up. You can have socially "conservative" people but still believe in communism. You can have socially "progressive" people that believe in capitalism, and vice versa.
After being on internet forums for years to me it appears there is an infinite number of positions on the socially "progressive", socially "conservative", politically communist and politically capitalist graph and on top of that those positions people hold seem to change as their circumstances and life experience changes.
In fact I would say you can not tell a person's true views by what others say about them, or even what they write in forums themselves as communication skills vary from person to person and comprehension skills vary as well, and emotions are not easily determined by written language.
But it seems some people cannot handle this constant changing flux of views and think, well such and such said this so therefore they absolutely are X, and these people are on all sides as well.