Nazi's are evil. People that correct grammar are annoying at worst. It is therefore a stupid term. It devalues actual evil and magnifies annoyances. Grammar is important, but comments should focus on the content of message first, unless the grammar errors or spelling errors make message harder to read or change the meaning of the message.
It's the rednecks that always try to correct people's grammar in an arrogant way. Remember this country America was on the Allied side. Nazis don't do that. Nazis actually use a lot of slang (the smart ones that is).
"Grammar Nazi" is such a stupid and dumb insult that it doesn't make sense.
"Grammar Nazi" really isn't a term as much as it is slang. "Nazi" just analogizes to a "controller" or a "guard"(or simply just "group"), as opposed to referring to an actual Nazi. Saying one is a Grammar Nazi is overall not really stupid, it is just slang meant to jokingly describe/group or stereotype people who would like everyone to have precise and proper grammar.