Since we all know the history of The Order, let's try to find out as much as possible about The Brethren.
The town of Silent Hill was found by the Brethren. The Brethren built most of the notable buildings in Silent Hill (including the school) and actively participated in witch-hunting. Also The Brethren often cites The Bible, including The Old Testament (All foes of the righteous will be condemned). All this may suggest that The Brethren was originally a form of Christian Puritanism.
Since time passed, destructive tendencies began to emerge within The Brethren. First of all, I can suggest that The Brethren had adopted some antitrinitarian ideas. As we can see in the school, The Brethren appear to worship some female deity. But they do not refer to it as goddess (like Claudia Wolf). It may suggest that The Brethren think of their god to be a some kind of inanimorphous being, that can take any form he like.
Arrogance. It had been the most notable thing in The Brethren. Members of The Brethren seem to think of themselves as of sinless people, unlike normal Christians, who know that no mortal is sinless. Even a few seconds before her death, Christabella do not repent, as any normal Christian would do - instead she asks for the strenght to «stay pure».
We fight the sin, not the sinners. It seems, that Christabella forgot about what a sin is. According to Christian teachings a sin is an action, that brings harm to a person, and violates the moral rule. Instead, Christabella thinks, that a sin is a person named Alessa. Of course she had forgotten, that Alessa is innocent, and Dahlia is the one, who had commited a sin and has to repent. Instead of that, Christabella just tries to get rid of Alessa as some material evidence of Dahlia's sin.
The church. As many other prominent buildings in Silent Hill, it may also had been built by The Brethen, but the church was most likely built before The Brethren had broke with Christianity. Also a conflict between the legitimate Christianity and The Brethren might had taken place some time before Alessa's burning for the ownership of the church. Of course no normal Christian priest would not serve in a church with a painting of a witch being burned alive instead of an iconostasis.
The Brethren may had been a cult, that was originally a Puritanical Christian organisation, but later had debased Christian ideas and turned into a destructive cult, with nearly no surviving elements of Christian teachings. Sister Margaret gets upset, while The Brethren is mentioned, and it is not only because The Brethren had burned Alessa, but it also may suggest that there was a serious conflict between The Brethren and legitimate Christianity.