but capitalism could, in theory, exist in a matriarchal society. This is exactly why discussions have to include intersectionality. You can't look at how a wc person is treated within capitalism without also looking at the effects of racism, homophobia, patriarchy etc etc. There's no such thing as a homogenous wc within one country.
Even discussing the intersection of capitalism & feminism is a very simplistic analysis. But, to sum it up - capitalism allows financial benefits to certain people. It rewards privilege and power. In a patriarchal society, it therefore elevates male above female.
If we wanted to discuss capitalism and race, we would conclude that white skin is more privileged and rewarded than any other color.
Could feminism and capitalism work together? Yes, in theory. If we could somehow do a mind wipe of every person on the planet, change history and make it so that we don't look at people and automatically categorize into male/female and then stereotype, pigeon hole and reward accordingly, then capitalism could be a place where everyone has equity (equal access to success, even if not everyone achieves the same success). BUT - there would have to be some very careful thought about inheritance.
Could capitalism and feminism work together in our current societies? Maybe. There are pressure groups, charities etc. If enough businesses start to accept that employing/promoting women is of financial benefit, they will start to do that. One area where this is being promoted is the Geena Davis group for women in the media.