Is There Such a Thing as a Lowercase "nazi"?

Inspired by an exchange on Facebook.

An editor friend posted a completely appropriate rant about the use of non-words such as "conversate" and "orientate", which some poor misguided people have created as backformations from "conversation" and "orientation" instead of using the perfectly good words "converse" and "orient." These people are very wrong.

In the ensuing discussion someone referred to her as the "grammar nazi."

After contributing the equally grating "administrate" to the list of nonwords to be avoided, I added this:

I'll also put in a plug for not misusing the word "Nazi". I lived in North Idaho where the neo-Nazis were; they chased and shot at acquaintances of mine simply because their car backfired near the compound, burned crosses, and held parades. They lost the compound in the resulting lawsuit after the shooting incident, thank heavens.

There's the real thing, and then there are people who are sticklers for one thing or another, whether it's soup (a la Seinfeld) or grammar. I'm a stickler for not using a word that means killing 6 million people to refer to people who have certain rules they follow because that diminishes the impact of the word when applied to the real thing.
To which someone responded:

I think the misunderstanding here with the use of the word "nazi" should be recognized thusly: "Nazi," with an uppercase N, refers to a group of people in Germany prior to and during the Second World War, who were acting out orders from a lunatic because they were cowards. In constrast, "nazi" with a lowercase n, refers to a group of people for whom rules an regulations are of utmost importance in a given subject.

Hence, "Hitler's Nazis" refers to genocidal maniacs and their pawns, and "grammar nazi" refers to a person for whom proper grammar, spelling, and syntax are of utmost importance and value.
It's the difference between a proper noun and a common noun.

You're welcome.
(As a professional editor I'll overlook the potential connotations of "You're welcome" and just address the underlying issue.)

I get the difference between proper nouns and common nouns. There are Democrats and democrats, Socialists and socialists, Stoics and stoics.

But are there really Nazis and nazis? Wasn't what the National Socialist German Workers' Party (its real name) did so utterly horrifying that we can't lowercase it and diminish the impact of its real meaning in historical context? I am a stickler for grammar most of the time but definitely not interested in being referred to as a lowercase nazi.