Very well put, and if there was a thread about the role of personality cults and tribalism in politics, a comparison with the Nazi Party could be valid. Jung had an interesting essay on the psychology of Nazism. That's probably the best sphere in which to debate those madmen.
If, however, we're debating along tradtional Right/Left lines, then comparisons are near-invariably smears. As has been said, the Conservative was probably trying to turn around the tired "Nazis are right-wing" smear-by-association, but maybe he was also bringing in no-platform, as you say, he didn't put his point over very well at all, whatever it was.