Money and capitalism in particular, tend to reinforce the dominance hierarchy but then I look at countries like Denmark that actively teach empathy in schools and that encourages students to compete against themselves rather than against each other. They are a small and rather homogenous country, but they have both a robust economy and a high standard of happiness. Democratic socialism can have it's own set of issues, but it does seem to be a much better fit for a more partnership-oriented social system.
One of my Medium frenemies often contends that socialism would put an end to racism and other sorts of inequality. I contend that this is an economic system and patriarchy is a social system. Although they certainly have overlap, I don't think changing one necessarily impacts all the aspects of the other. I've been wanting to write something about that, but just haven't gotten that far yet.