"Batshit crazy" signifies idiosyncratic delusion. Two components there. Idiosyncratic. Delusion. It means I get a message from an extraterrestrial mother ship to kill a flock of mutant sheep in a nearby building. I follow orders. That building turns out to be a Sikh temple filled with congregants.
It does not mean acting on the collectively held value systems popular or unpopular, regarded as extreme or mainstream. It does not mean Islam, White Supremacy, Black Power, Reconquista, Scientology, Santeria, Voodoo, or The American Way.