Church - to be honest, BoC society is quite similiar to early American - it consist mostly of immigrants. Not many chars (at least of those, which have their bio posted) are said to "born" in Cove. That's why not everyone feels the need to follow the Avatar - they came from more or less distant lands with their own habits and beliefs. If you don't respect Avatar, you don't respect his organisation. Presto. Even more, when that organisation is preaching using sword and whip.
As far as I know, all the humans worship the Avatar (or the Guardian=P ). It's how it is in Sosaria. And the Church in the middle ages christened heathens with the sword, and it creates a certain realistic aspect. The Church could perhaps come to some deal with the Church of Yew, letting them hold masses in Cove?