Both sides calling the others Nazis doesn’t imply that centrists are using critical thinking. It just means that one side is lying. Nazism is a far right ideology.

“Never believe that anti-Semites are completely unaware of the absurdity of their replies. They know that their remarks are frivolous, open to challenge. But they are amusing themselves, for it is their adversary who is obliged to use words responsibly, since he believes in words.”

— Jean-Paul Sartre