Why would anyone think that Palin, a staunch Conservative, be a sympathizer of the "National SOCIALIST German WORKERS' Party"?
Yes, The NAZI movement was a SOCIALIST movement.
When the “American” “Progressive Left” had to make a choice between Stalin and Hitler,
they threw in their lot with Stalin and from then on branded the Nazis as “rightwing” and “conservative”.
Communism and Fascism are at their heart the same thing (collectivist); they were just competing for the same ideological mindset and had to demonize the other.