Content Warning: This article contains links to archived copies of far-right web-pages, as well as discussion of extreme racism and far-right ideology.
A central question in Judaism is “Who is a Jew”? It follows that a central question in anti-Semitism ought to be “Who is a Nazi”? Without a doubt, members of the 1920-40s National Socialist German Workers’ Party were Nazis, although it should be noted that they didn’t call themselves that — it was a derogatory shorthand sort of like “commie.” But everyone calls them that now, and if there's one group of people it's ok to disrespect, it's them. Presumably, it’s also ok to apply the terms "Nazi" to their voters and any moderately high-ranking military/government officials in Nazi Germany.
We can also probably include parties that are explicitly modelled after the original Nazi party. For instance, there’s a currently-existing American Nazi party. It would be a bit silly not to count them as Nazis as well, although in an academic paper or something, you probably want to specify that they are Neo-Nazis.
There are some parties that have a more complex descent from the original Nazis. For instance, the British National Party was founded in the 1980s by members of the 1960-70s National Front, which was founded by members of 1930s British Union of Fascists, which was directly affiliated with Fascists in Italy and Germany. It feels like these people ought to be called Nazis, but their relation is sufficiently distant that they probably can’t be in a technical sense.
Then we have people like Richard Spencer who don’t explicitly identify as Nazis but who think that the Jews are the ones thwarting their effort to establish a white Aryan ethno-state and who say things like “Heil Trump. Heil our People” while giving a Nazi (or “Roman”) salute. Admittedly, Spencer claims that he wants a “peaceful ethnic cleansing,” but the original Nazis said so until they actually got into power. The original plan was to deport the Jews to Madagascar.
I also have to reluctantly say that people like Spencer can’t formally be called “Nazis,” because they do represent a clearly separate political movement from that of Adolph Hitler — albeit one with many of the same insidious beliefs. They call themselves “alt-right,” which is fine once you learn that it means “practically a Nazi.” This term was useful for a while, since at one point the only place you could learn the term was someplace like Metapedia, where you would also learn that Wow, there are actually people who still think Hitler was the Good Guy and they have their own Wiki!
But then in 2015, these people all rallied around Trump’s presidential campaign and got the attention of people who don’t spend way too much time online reading stuff written by crazy people. The reporting came mostly from outlets like Vox and CNN, which tried put forth their journalistic due diligence and be fair to the people they were reporting on, which of course had no effect on the public perception that everything they say is slanted to the left. The result is that there are a lot of people who think that the Nazi stuff is just exaggeration and that “alt-right” just means “solid Republican voter.”
Therefore, I think it’s better to just call a spade a spade. But you should be clear that the term is informal, when used for people like Spencer and the BNP, by writing “nazi” with a lower-case n.
You should avoid using this term indiscriminately, because a lot of people have been trained to assume that the term “nazi” is hyperbole. In fact, a lot of traditional conservatives have hilariously gotten used to assuming that anyone being called a “nazi” is on their side, and are often fooled into coming to the defense of actual nazis. However, I don’t think this is as bad as confusion over “alt-right,” because that’s effectively a neologism, whereas “nazi” fundamentally has to mean someone with extreme right-wing, racist, and anti-democratic beliefs – so if you use it exclusively to mean that, and someone assumes you’re talking about a traditional conservative, then it’s their fault, not yours.
My recommendation is that “nazi” should be reserved for people that do at least half of the following: