You mentioned that believing in a complimentarian dynamic doesn’t have to drive marginalization and abuse of women — but it does in a dominance hierarchy context, which is what patriarchy is (and we see this is how it plays out in reality), because saying that women are inherently other is saying that women are less, not as smart, capable, worthy of power, etc, as men. That they exist to birth and care for babies and to take care of the needs of men. Men are the ones designed to go out into the world and act upon it — women are not. When you teach “men are like this” and “women are like that” which is very different from men, not only does it make it hard for the people who don’t naturally fit with those descriptions, it sets up control and marginalization of women as natural and inevitable.

In an indigenous culture that instead says, “women do these jobs” and “men do these jobs” but whatever you want to do is fine, as long as you contribute to the group, there tends to be more of a balance. In many of these tribes, the men do have political power, but only with the advice and consent of the women. Patriarchy is fundementally a dominance based hierarchy where egalitarian cultures have structures for keeping a balance of power.

Here's an example related to Southwestern Indian tribes:

"Women typically owned the houses and land; men moved into their wives' houses at marriage, and if they divorced, the husband had to leave. Men were in charge of war, farming, government, and ceremonial societies. Pottery, weaving, and jewelry-making were normally assigned to either men or women, but these roles varied from tribe to tribe. Many of these gender roles persist to the present day."

https://www.amnh.org/exhibitions/totems-to-turquoise/society/gender