Venice, swiss and Genoa would be another 3, they did have a religion but it had no power, cardinals and priests where assigned only by each republic and not on the order of the papal states.
So, if the religion is powerless, then we need a "secular" religion or name it something else.
Switzerland historically did have some sort of state religion - they even had a civil war between the protestant and catholic cantons.
http://en.wikipedia.org/wiki/Reformation_in_Switzerland
And no religion in the game has anything to do with who assigned the bishops. A catholic state would be catholic regardless if the bishop is assigned by the emperor or the pope. That difference only means that the state was somewhat independent from the popes commands but not that it had a different religion or even was a secular state. Concordats between states that regulated how much influence the pope had in different countries were common:
http://en.wikipedia.org/wiki/Concordat
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