Catharism is a well-studied topic, and while you are waiting for fresh responses to your question, it is well worth reviewing this earlier thread, led by u/sunagainstgold, which looks at the the history and historiography of the supposed heresy, and points out that our understanding of "Catharism" is really a construct imposed by the outsiders who persecuted it, adding that "medievalists today are pretty unanimous that there was no such thing as 'Catharism' in southern France in the 12th-13th century."

Sun does also touch on the specific area of gender relations in the time and place that you're interested in.

Meanwhile, and in the same thread, u/idjet (who was writing a dissertation on the Cathars) pushes back in posts that argue for something more approaching the old standard view of Catharism as a distinct set of real beliefs.