The story
First use appears c. 1991. From grammar + Nazi (“one who imposes one's views on others; one who is considered unfairly oppressive or needlessly strict”).
Etymology from Wiktionary, CC BY-SA 4.0.
grammar nazi
gram·mar NaziToday it means: A person who habitually criticizes the grammar and (often) usage in others' speech or writing, often in ways that are sometimes not even linguistically accurate. Full definition →