Not neutrality on his part. He’s saying that this isn’t a party thing, that it is bigger than that. That all the clowns in DC are screwing us over, not just a particular party. They are all playing on the same team—team “Them”.
How is this not a 'party' thing? The democrat party is a leftist party. He says he is neither left nor right. Everything he complains about in the song is the direct result of democratic leftist policies. Sorry, he sounds like a naive fool.