The group that Lindbergh supported was not the Nazi Party -- it was the America First Committee (the leading an anti-war group prior to WWII). Lindbergh was not a Nazi, but he did believe in eugenics, racism, the superiority of America and Europe, was against war involving America and any western-European countries fighting each other, and was against communism. Other members of America First included Sinclair Lewis, Walt Disney, Gore Vidal, Gerald Ford, and 800,000 other Americans, and support came from presidents/founders of some of the largest corporations in the US (Sears, Morton Salt, New York Daily News, Chicago Tribune).
So, it wasn't a fringe group made up only of crackpots. Nor was it a Nazi organization. If anything, it was more communist leaning since it was allied with the Keep America Out of War Committee, formed by socialist Norman Thomas. Prior to Germany's invasion of the Soviet Union, Germany and the Soviet Union were on the same side, and the Soviets didn't want America in the war. They supported America First and Keep America Out of War. Once Germany invaded the Soviet Union, that stance reversed, the Keep America Out of the War Committee reversed its opinion, and the Soviets put out propaganda accusing America First of being a Nazi front.