People say "invoking Godwin's law" as if that person is demanding the conversation halt there - but I very rarely see this happen in practice. It's simply an observation. "Oh, we compared them to the Nazis". In decent discussion fora such as this one I almost never see an associated suggestion that the argument is invalid, or that discussion should end.
There is an oft-cited corollary, sometimes misunderstood as part of Godwin's Law itself, that whoever brings up Nazis first automatically loses the argument. In practice, it really does shut down discussion amongst even otherwise intelligent people, usually by preventing people from making comparisons in the first place.
