Would a catastrophic defeat in Norway destabilise Hitler's rule?
Short answerProbably not; Hitler could blame the navy, but the defeat might end Germany's surface-fleet program.
NotesOne naval disaster is unlikely to remove Hitler after the victories already accumulated by 1940. The regime could redirect blame toward the Kriegsmarine and possibly Admiral Raeder instead. The more consequential institutional result could be cancellation or abandonment of the surface fleet, including Bismarck and Tirpitz. That would free British capital ships for other theatres even if the political leadership in Berlin survived.