Part of it is that Nazis and Communists (with a capital C, usually taken to be communism in the Chinese/Korean/Soviet sense) fit the "bad guys" archetype in American media (or - more precisely - said archetype developed in response to them being our adversaries in WWII and the Cold War, respectively). Naturally, that means accusing someone of being a Nazi or Communist is an effortless way to paint that someone as a pure and classic villain.

Now we have people overtly and brazenly affiliating identifying as Nazis (usually citing The Bell Curve and other pseudoscientific racist drivel) and Communists (still with the capital C; they might claim to be lowercase-c communists or plain socialists, but it doesn't take long before "Stalin did nothing wrong" or "China's more ethical than the US" starts peeking through the façade). Both have always existed, of course (at least as long as those ideologies have existed), but nowadays folks are more open about their abhorrently-anti-democratic viewpoints (especially on the Internet, where they enjoy relative safety while simultaneously reaching worldwide audiences).