Saying I'm a Nazi and going on a Nazi-organised march, I'll accept their claims.
The think to keep in mind with all this "Schroedinger's Nazi" nonsense, is that there is a very clear and obvious reason why it's occurring, that isn't really being addressed. That the "Schroedinger's Nazi" people have a vested interest in creating this false distinction, it's not just random denialism or "skepticism".
That reason is
cognitive dissonance.
They know that Nazis are evil, or at least that the overwhelming majority of society considers Nazis evil, and have the history of mass murder on an unprecedented scale to demonstrate how evil they are.
However, in the case of neo-Nazis and others in the so-called alt.right, they also see parts of themselves. They can see the similarities in worldview and philosophy, shared beliefs if not necessarily shared goals. They are unhappy with the changes that are going on in the world, with louder voices being given to marginalized groups, with their own comfortable privileges being challenged; and they are not happy with that. Change is difficult, and they feel like they're losing something important to them. The status quo is being torn down, and with it their social standing.
So when they hear the neo-Nazis and KKK and other white supremacists and nationalists and fascists going on about the same thing, only taken to a much more violent and sinister level, this also makes them uncomfortable. They can see the logical links to their worldview in the fascists' worldivew. But in their minds they cannot be similar, because they are the "Good Guys" and the Nazis were the "Bad Guys"; and of course no one believes themselves to be the "Bad Guys". They can't believe themselves to be the "Bad Guys".
So since they do not wish to be associated with the fascists, that presents them with two options: 1) change their own worldview, or 2) deny the existence of the fascists. Changing one's worldview is extremely difficult to do, and they don't really have any desire to change it since it's so deeply ingrained, its something they've believed since they were old enough to have beliefs. Few people ever really change the worldview they were raised in; at least not quickly, and rarely completely.
So the other option is to deny the neo-Nazis. Obviously they cannot deny the obvious evidence that everyone can see (unless they're Trump), cannot deny the existence of people walking around with swastika armbands, cross-and-shield, white hood, etc. But what they
can do is deny said peoples' links to the Nazi worldview, the historical KKK, and so on. They downplay the link, try to deny the heritage; and in doing so come up with dissonant distortions of logic accusing the fascists of being "cosplayers", "edgelord trolls", "No True Nazis", and so on. Denying that these people really understand or believe in the images and philosophies that they're "playing at".
And, of course, in order to maintain this state of mind, they must also denounce and deride those who stand up to and oppose the fascists. If someone treats the fascists as a real threat, as truly believing in and practicing the fascist white supremacist worldview, that threatens their own logical balancing act and forces them to take the neo-Nazis seriously, which their self-image will not allow them to do. So the anti-fascists become the true enemies, and must be demonized and ascribed the qualities of those they are opposing in order to maintain the facade.
Thus they resolve their cognitive dissonance and preserve their own worldview, without having to resort to uncomfortable and difficult self-examination in the face of growing evidence. They get to keep seeing themselves as "Good Guys", despite their clear similarities to the "Bad Guys".
