Don't get me wrong. The current Equalist movement is created in Amon and Kato's image. Angry, vengeful and violent. That isn't Asami's way.
I think Asami might create a new Equalist movement that is largely non-violent in nature, an organization that truly strives to give non-benders a say in how their world is ruled. However, I suspect Korra now has a bias against any
Equalist movement, which would put Korra and Asami on different sides. How they resolve their differences, is something I would love to see. Would they physically fight each other, I hope so :P but I think ultimately Korra and Asami would come to respect each other's perspective and work out a compromise that is beneficial to both benders and non-benders.