Not only do some branches of feminism openly support Marxist ideas, I can kind of see how critiques of feminism suggest a close relationship to Marxism: What makes Marxism ideological (let’s say that means “ignorance of evidence/arguments for the benefit of an ideal”) because it is ignorant of the possibility that the ruling class actually solves problems for everyone. For example, the ruling class is approximately and implicitly selected to have good genes: it is smart and healthy; making it fit for rulership and innovation. In a world with limited resources it is a fairly important question who can make the most of them. Capitalism solves this problem imperfectly but robustly by decentralized, hierarchical sortation based on material incentives.

Analogously to Marxism, feminism assumes the patriarchy (the ruling class analog) only exists for its own advantage and does not solve important problems for society at large. There are, however, problems it does seem to solve: (1) it allows for early specialization on domestic tasks by women (cooking, socializing etc. which are not trivial at all. Today, nobody really specializes on this anymore which contributes to the modern community problem), (2) it channels men’s aggression in fierce competition in a way that benefits the economy and therefore the entire nation, (3) marriage (if you count that as patriarchal) likely solves issues with inclusion of aggressive males, (4) it allows men to gain material status which men but not women need to succeed at a personal level, and (5) it keeps the birth rate of the ruling class/healthy and intelligent at a high level.

For another example, look at how computer programming used to be considered a lowly, secretarial job in the early 20th century, but once it became dominated by men it became a highly paid, prestigious job.

It seems the causality arrow goes exactly in the opposite direction. With the raise of IT giants like IBM and Microsoft, the field became prestigious and men aim much more aggressively for positions with high prestige for the silly reason mentioned in point (4). It’s not like the programmers became better paid because it had more men in them. They became better paid because people realized the importance of digital information processing, so people could pull in a shitload of money.