Hate groups, according to the Southern Poverty Law Center, "have beliefs or practices that attack or malign an entire class of people, typically for their immutable characteristics." This precisely defines the Moms Demand Action group.
The belief in the Second Amendment as it is written is not a religion, but it is a belief, which is an immutable characteristic. Coupled with their members' intense hatred and wishing for violence towards an entire class of people (legal gun owners), they precisely follow the FBI's hate model. They gather, they define themselves (with logos, slogans), they disparage their target, they taunt their target, they attack their target with and without weapons (verbal), then they destroy their target. They need to be classified as the hate group they are.