There is a word anti-partyism, but it doesn't seem to be commonly used.
The literal answer to your literal question is called "believing that US politics should be non-partisan".
https://en.wikipedia.org/wiki/Non-partisan_democracy
The US started as de facto non-partisan democracy. There is a de jure option.
https://en.wikipedia.org/wiki/Direct_democracy
Direct democracy would probably give less power to political parties, but there still could be voting blocs. An example:
https://en.wikipedia.org/wiki/Orthodox_Jewish_bloc_voting
Modern thinking says an alternate etymology is more likely, but it certainly existed long before it took on the meaning from the story.
https://en.wiktionary.org/wiki/%E1%BD%88%CE%B4%CF%85%CF%83%CF%83%CE%B5%CF%8D%CF%82#Ancient_Greek