Yes, it is hard to pinpoint exactly what makes one an American. It is not hard at all to pinpoint what makes one an X for any given European nation. It is strange how much Americans project our weak identity to the rest of the western world.
Except: exactly the same rhetoric is being used by the far-right in America as it is in Europe and the Anglosphere. Strength or weakness of identity is irrelevant to the white nationalist project.
What epistemic value does "similar rhetoric" have? The relevant question is whether something is true and/or defensible. Identity does matter, to some nations and historical contexts more than others. It is silly to project the particulars of the US historical context to the rest of the world.
That doesn't answer the question. Identity does matter. Because Nazi Germany came to the wrong conclusion does not invalidate every premise used in their justification.