A religion of Arbre, likely analogous to Protestantism on Earth.
Orthodox religion is referred to as "Bazian," and there are several references to the fall of Baz, which was apparently the home seat of a large empire. There are several candidates for analogues to Baz; the most likely appear to be Rome and Constantinople. Despite the fall of Baz, a number of people still count themselves as "Bazian," and the religion apparently thrives. There is mention of a Bazian nun who is also a schoolteacher; she leads the children of her suvin, identifiable by their uniforms, through the tour that Erasmus gives of the museum and artifacts housed in the Unarian math. (Since this museum appears to be accessible through the Unarian Gate and not the Day Gate - as some of the concent's facilities are - it is probably not open to the public except during Apert.) A Bazian monastery is also mentioned; Erasmus and part of his Convox group shelter there for a night. "Bazian" religion, then, would appear to be analogous to Catholicism.
If this is the case, then "Counter-Bazian" is indeed analogous to Protestantism, and like the word "Protestant," "Counter-Bazian" is an umbrella term for a large number of religious groups which hold beliefs that generally recognizable to one another and to Bazian, but which are irreconcilable with either each other or with Orthodox Bazian religion. Two distinct Counter-Bazian branches are mentioned: the 'Samble' ark, which developed around Saunt Bly (who was himself agnostic or atheistic), and the Warden of Heaven's. The Samble ark - which, according to faithful member Gnel Crade, is dying - is the progenitor of the Warden of Heaven's ark; it will be discussed first.
The Samble-ites (for want of a better word) believe in studying ancient texts in the original language, which is Orth, rather than popularly-spoken Fluccish. Crade, and very likely most of his co-religionists, have taken it upon themselves to learn Orth, though Erasmus calls Crade's spoken accent "wild," suggesting that he had little formal instruction in the language. The emphasis placed on reading holy texts for oneself without a mediating priest is strikingly similar to Lutheranism. (Luther, incidentally, was a friend and correspondent of the Humanist philosopher Erasmus.) Crade says that his group was well aware that Saunt Bly did not believe in God, but they feel a kinship with his struggle. Fraa Erasmus' group arrives during a religious service, and though they remain outside of the ark, they can hear passionate singing. Crade later tells Erasmus that his religion is dying off, slowly being killed by an offshoot which has recently grown very popular: the Warden of Heaven.
The Warden of Heaven - whose self-given title is reminiscent of the titles of mathic hierarchs - claims religious descent not from the Samble ark but from the maths: he claims that he brings 'proof' of the existence of God which the mathic world - with the possible exception of the Millenarians - is trying to hide. He dresses in roped robes which mimic the bolt and chord of the avout. Unlike the Samble ark, which stresses learning (although not theorics), the Warden of Heaven tells people what to believe, thus acting as a mediator between his flock and God. The Warden of Heaven's ark does not otherwise appear to resemble traditional Bazian orthodoxy. It is hinted at the end of the book that the Warden of Heaven's ark has fallen into disarray following the Warden's death; Barb's father, Artisan Quin, mentions that his cousin, Artisan Flec, is lost religiously, but also has no desire to study: he simply wants to be told what to believe. That the Warden of Heaven's ark is apparently collapsing suggests that the WoH made no, or at best unpopular, choices for his succession or the continuation of his ark after his death. The manner of his death, and his half-heard conversation with Jesry shortly before it, suggest that the Warden was not a particularly forward-thinking man.
Erasmus encounters another religious group, the Kelx, though they do not appear to be related to or an offshoot of the Bazian religion, and instead focus on the Magistrate, the Criminal on trial, and the Innocent who was one of the Criminal's victims.
It is not known what religion Laro and Dag subscribe to; they do not appear to be related to Bazian, Counter-Bazian, or Kelx. Their belief that the avout cast spells, and Laro's interpretation of Erasmus' actions to save Laro's life, suggest a deeply superstitious belief system in which all avout are regarded with outright hostility.
For their part, the avout have a tendency to refer to anyone who believes in God as a "Deolater," including those avout who profess a belief in God.