Feminazis want equal pay for equal work.
Smoking nazis want to be able to breathe air without being polluted by the nearby person's cigarette smoke.
Grammar nazis would simply prefer that people use the appropriate words for the correct situations.
Real nazis killed over 6 million Jews and Polacks simply to assert their racial superiority (while worshipping someone who would have been killed under many of their own criterion), and to this day continue to rally for an oppressive, fascist state made up of one master race.
Ahh, hyperbole at work.