Following my previous question,
I decided that a power that could oppose a King was facilitated by having a religious component. The idea is to have one of the main land-owner, the local head of a Church, similar to Prince-Bishop of the Holy Roman Empire. Due to the land he controls within the Kingdom, he is one of main "Peer of the Kingdom", and as he is as well a key person in the religion of the country, he has ways to get the support of the local population, which amplifies his opposition to the King.
Now, I am trying to build the said Church and Belief, but due to the examples I referenced above, only the Christian Church come to my mind. However, I don't want to make any statement or judgement on the Christian Faith at all within my story, so I'd like to design my Church not to be too identifiable with any existing Church.
The easiest that come to me, and are quite common in Medieval Fantasy is to set a polytheist religion. Unfortunately, the examples I can think about are typical animist religions like the Norse, Celt or Shintoists religions, which were, to my knowledge, quite unorganised, and the typical Greek-Roman Gods. But there, one had to choose to be a priest of one or another God, and no God were really taking over the others.
Can a polytheist religion be organized in a similar way as Roman Catholic in the Middle-Ages, as far as its relation with power control is concerned?
To clarify a few points, you can see above, that I am interested in a Prince-Bishop-like figure who would hold considerable (open) political power as well as moral due to his position within a given religion.
In principle, the Sevens' Faith from A Song of Ice and Fire is a bit in the direction that I would like to have, but GRR Martin hasn't been always lauded for the realism of his world. And I am not aware of any similar Cult/Religion existing or having existed in our World..?
A note, stemming from one of the anwer, I am interested in a Church as a purely political organisation. That means that they have an influence in the population who believe almost entirely in the presence of some Gods. But I don't want said Gods to go around, strolling the land doing a few miracles here and there.