Is “Godwin’s Law” or a version of it invoked in Europe if someone brings up Hitler comparisons in situations that are not validly related or comparable to Nazism/Hitler?
Sure. The part of Usenet where Mike Godwin posted his law was never meant to be limited to any one country.
I guess the question really is, is there anywhere in Europe where some else’s name trumps hitler?
I’m confused. Presumably you’re not under the impression that people in Europe have not heard of Hitler, or that he’s a popular figure there. Do you think they would be to polite to mention him, because it’s too close to home? Or what exactly?
What I mean is - there tends to be a backlash in America when someone brings up Hitler or Nazism as a rhetorical weapon in debates or discussions where Hitler or Nazism isn’t a valid comparison.
Is there a similar backlash in European discourse?
Godwin’s Law isn’t a law as much as an observation.
It’s the observation that when one or both sides are resorting to literally the most inflammatory insults they can think of, the discussion is over and it’s now just a shouting match. He just used “Nazis” as a convenient example of a group which was, in his mind, universally loathed in his social context. In other contexts, it could be “gays” or “Christians” or “Muslims” or “cishets” or any other identifiable category.
The group doesn’t matter. The intense vitriol matters.
So you’re asking, what comparison is made in Germany and Austria, for excessive dogmatism, that means you’ve all gone too far? They use Hitler.
Why wouldn’t they? Why would Britain, Ireland, Norway, France, Spain, Italy, Greece, the Isle of Malta not? Can you name another nation in the Eurosphere where Hitler is too weird to mention?
One difference with European nations is that some speech, especially Holocaust denial and advocacy of Nazi ideals (hate speech) is illegal.
So I guess the European variant of Godwin’s Law might be that the conversation is over because one or both sides were arrested. 
Since Hitler and the Nazis are ancient history to most people on the net, I notice a new hate figure is taking over.
Justin Bieber?