I'm not accusing either of you of being Nazis, you know? No need for this game of terminological keep-away.
But look, the fact is that, by most people's definition, Nazism is definitely a far-right ideology owing to the severity of its racist attitudes. Left wing and right wing politics are distinguished primarily by their attitudes toward equality. A set of politics belongs to the left to the extent that it advocates equal relationships between people (and perhaps also between human beings and nature). A set of politics is right wing to the extent that it advocates for institutionalizing unequal relationships between people or exterminating "inferior" groups. That's how people generally think about it. In fact, to this end, I could also make an argument about the supposed left wing credentials of Hitler's
top-down idea of "socialism", but as much is really beside the point here. The point is that is that Nazis are people who only use and twist economic populism to service extraordinarily backward, often genocidal attitudes toward people of other races. They use feudal imagery and often believe in slavery, rape, and genocide as matters of principle, etc. If you don't believe me, here's the
Wikipedia article defining the term "far-right politics". It's NOT just my opinion! That's just how politicos have broadly chosen to define it.
You're right in the sense that, Representative Steve King notwithstanding, the relationship between the Republican Party and the neo-Nazi movement is essentially non-existent, and also in the sense the American neo-Nazi movement opposes American constitutionalism on principle. But it's absence from
the mainstream of the conservative scene in this country doesn't mean it's not a conservative movement. It definitely is. Neo-Nazis
define themselves as conservatives. Reactionaries actually is the more common term they use. That's their opinion of themselves, not my hot take.