Polygamy Polygyny, in particular, is a largely religious institution. In no small part that’s due to the fact that polygamy polygyny is inherently patriarchal, and nearly all modern religions are too, so it makes sense that it would be found predominantly in religious communities and histories.
Polyamory, however, is neither patriarchal or matriarchal. It is freedom for everyone involved to have relationships in any capacity they want, including women and other non-male gendered people to be with whoever they want. Patriarchal societies will never accept something that gives women that type of freedom and power over their own lives.
Edit: I got some terminology wrong and thought polygamy was one man multiple women, but the term just refers to having multiple spouses. Polygyny is one man multiple women. Which def means I took the conversation down a weird hole.