EU referendum, brexit and the aftermath

Having a word in your name does not make you that thing.

Right, but when you embody parts of a concept it does then form part of your identity.

Just because it's an uncomfortable connection given your political persuasion, doesn't make it untrue.

Nazis were not socialists.

The NSDAP emerged from the DAP, a small Munich-based grouping of nationalists (complete with anti-semitist and other such tendencies) who supported some socialist-style policies but were at pains to stress that they were not Marxists. They were completely obscure until Hitler joined. There were leading Nazis, like Gregor Strasser, murdered in 1934, who were quite strongly socialist while being an anti-semite and racist, etc. (and whose murder was probably related to his political conflict with Hitler over this), and policies to that effect were in the NSDAP's manifesto for a long time. I don't remember when it was revised or whether it was quietly dropped, but German industrialists came to arrangements with Hitler as he got closer to power that ensured that of socialism not much, if anything, was left by 1933, or indeed enacted.

Still, it is an interesting lesson that we're seeing repeated to some extent in that the political spectrum allows for the existence of people who combine nationalist or racist with 'socialist' policies, or, at least, policies traditionally associated with the 'left'. (Whether they would do anything about them once in power is a rather different question--I think they use 'socialism' to tap into the strong discontent caused by inequality to deliver just the votes required to swing the balance, as we've seen with Trump or Brexit, while the main part of their electorate is made up of 'traditional' rightwingers.) One model that I've seen talked about recently is the 'horseshoe' model, in which the open end of the horseshoe represents the two extremist ends of the spectrum and the horsehoe's loop represents the 'centrist' aspect. I think that model doesn't go far enough--I think there's a continuum that closes the horseshoe. I've sometimes read about people who have moved from one kind of extremism to the other, without passing through centrist positions on the way, e.g. Marxists becoming Nazis and vice-versa.