There's no reason to assume that. The system could be destabilized because while a pendulum with two sides has a stable a world with many many competing interests and nonlinear feedback systems might not.
I'm not worried about a matriarchy either; what I am worried about is a permanent state of cold war between identity groups, which is where it seems we're headed.
This is a gross exaggeration. Power struggles have been with us since the beginning of time.
Men and women will get along as they always have, with ups and downs. There are no "identity groups" because we aren't and can't be enemies. There are just a few loonies on both sides making a ton of noise, and they're getting amplified by the internet. They'll either get boring at some point or just be ignored completely from the outside of their circles.