Is the Pope to rule America? Good OP, Athena. Very interesting.
If I didn't understand you wrongly, you seek a state that is secular -or at least - the most separated of religion. I agree that religious groups used to tangle with political groups, and specifically, to the right or far-right of the political arena.
I guess it is due to the reasons which a Catholic/Protestant or Christian Nationalist shares with the right faction: tradition, Christian values, heterosexual marriage, Western predominate, etc.
It would be weird to see a religious group supporting the left. They didn't do so, and neither will do. They are aware leftists are progressive and this means they are against the traditional values. Then, it is obvious that if Catholics or Protestants have to get into politics, they will go to the right wing.
This is why Christian Nationalists are cheering the people to vote for Trump. Here the same happens. I live in a Catholic country, and it is obvious that the Episcopalian Confederation is Conservative, and they ask to vote for the right.
It is fun when Protestants prevented Catholics from having power because they are more 'liberal' (?)... but at the end of the day, they share the same political ideology and even lobbies! AKA Christian Democrats: sceptical stance towards abortion and same-sex marriage, opposition to capital punishment and assisted suicide, the prohibition of drugs, opposition to secularisation, opposition to state atheism and a rejection of communism.