>A racist, especially a violent, right-wing one.[0]
Oxford Dictionary has an even broader definition[1]
As noted by other users, "brownshirt" is also used to describe "anyone in authority."[2]
I actually debated writing "pedantism nazi" instead of "grammar nazi" because I knew you would make that exact argument that grammar is not relevant. I also considered "semantics nazi" but decided against it as semantics is "the study of meanings"[3], but it is clear that you are actually more concerned with creating records of fault and "ignorance",[4] while you allow yourself to define GP's transgression in vague terms like "equate" meaning anything from regarding as equal or equivalent to "comparable"[5]. You claim that the meaning is unambiguous yet this nonexistent second meaning is so prevalent that GP had never heard of the first one.
[0] https://ahdictionary.com/word/search.html?q=Brownshirt
[1] https://www.oed.com/search/dictionary/?scope=Entries&q=Brown...
[2] https://urbandictionary.com/define.php?term=the%20Brownshirt...
[3] https://merriam-webster.com/dictionary/semantics