I had never thought to write something like this, but recent conversations with fellow DMs and some players made me realise sometimes one wants to know more deeply some "background" of this setting, giving for granted some things even in the books are left on a "vague" stance just to give all of us some freedom of interpretation.
I am not a thelogist myself and I am also agnostic real life, nevertheless my studies often took me within the range of this subject and, furthermore, I live in a Catholic country where I was baptized 37 years ago, I could walk and be in 30 minutes in St.Peter, and even in a time of history in which spirituality is often overcome by other needs, the sense of Christianity is always alive around myself. What follows does not yearn to be any extensive project on history of Christianity, but just a short layout, shorter even than what you can find on any wiki-similar pages. But what I would like stressing is the similarities with Ezra in our canon.
Christianity, as we all know, was born as sect of Jewish religion, around the 1st Century CE. Gradually, after persecutions but stubborn resistance of early Christians, they managed to become the main religion of the decaying Roman Empire under Emperor Constantine I (about 300 CE). From then Christianity has been the -only- authorized religion in Western Europe, a state religion basically, where politics and real spirituality often mingled. The only dangers for them were Islam and the heretical thoughts: the first caused the infamous Crusades, the latter were at first suppressed just to spread in a stronger way in the dawn of Reinassance (1500 or so, Luther). It is clear that for almost 1200 years Christianity has been the only religion in most Europe, the views of Popes and politicized bishops caused wars, struggles, economical dealings (for instance the conquest of the "New World" which was authorized only for Spain and Portugal). Basically for every King or ruler, being excommunicated meant losing the sense of "anointed by God" which only the Church could provide. Political power had dealings, constantly, with the Church, and vice versa.
And Christian Church was highly militant because one of the teachings of the Gospels is to spread it. Thus, in every new place where early Christian preachers went, they tried to combine local customs and own dogmas. It is not a secret that some modern days Christian holidays are based on "heathen" festivities, like the period of Christmas, Halloween, et cetera. The only -art- which was possible was the one related to God and Christ, and Mary, and the Saint. Most Europe still has many of those artworks, the gothic and romanic churches, the paintings, the few sculptures: even works inspired to the classical myths of ancient Greece and Rome had to be interpreted always in Christian terms. Church supported also the birth of theatre with Mystery Plays, Miracle Plays, Morality Plays, all useful ways to spread the religion to those parts of the population who could not read. The believer could not interpret anything by himself, it was always filtered by the words of the priest, who had, himself, the "line" provided by bishops, cardinals and to some higher degree the Pope himself. Whoevfer had doubts, and dared expressing them, could be easily addressed as heretical, heathen, and be killed in the name of God. You all know the story of Joan of Arc, who eventually was turned into saint, but at that time was pointed at as witch.
Something partly changed in the Reform and Counterform periods, when scholars like Luther and Calvin spread different interpretations attacking directly the stucture of the Church (if you like history maybe you can find also the other reasons, besides the spiritual ones, which led to the success of the Reform). Some countries remained "real Christian" or Catholics, others turned into Protestant countries, all believing in the same God and most of the dogmas, but with different and detatched stuctures. But Luther and Calvin were hereticals from the Catholic point of view. Catholic countries became "darker" with more inquisitorial processes, hereticals were hunted in many counties: in some, like England and Flanders, the situation was better (in England it was worse for Catholics). Groups of them moved to the Americas to find the promised land, the New Jerusalem (from hence the name Salem comes), and with less and less control (and opposition) of the structure of Catholic church basically had the chance to become a proper different religion, even if, I repeat, they shared most dogmas, scriptures, et cetera. The break of the Reform was bigger than other reformist movements which existed in the Church in Middle Ages: for instance, St Francis, who proclaimed a need of a return to a poorer state for the Church, had the need to go to Rome to be aknowledged by the Pope himself, not to be pointed at as heretical.
Church of Ezra is loosely based on all this background, it is quite easy seeing how the different sects can remind us of some of the changes in the history of Christianity, how the political power is almost the same, how the church in time has tried to keep its power also when it was fading. Let's say, if we want to tease the comparison a tiny bit, the Church of Ezra is similar to 1500 period, when a first schism had happened (st.Francis, but within the ranks of the church/the Pure Hearts, LG sect) and when nevertheless had to deal with inner and outer heresies, trying to involve them within the Church itself (the process of creation of a new sect, with the new scripts etc.). As a matter of fact, as rule of this server, we don't allow Gothic Earth characters past 1650: it's the age when Reform/Countereform were fading, not yet in the Enlightnment period, but moving towards it, but an age in which the religious sense covered all aspects of the life of an individual.
It is the sense of the Church before 1600 that we must put in count when playing with/against a religious faction as Ezra, not our modern-days view, and as I said I am agnostic myself so I actually care not a lot about what the Church states. This is true not just for Ezra, D&D and Ravenloft are settings loosely inspired to the Middle Ages, not to nowadays: atheist people in the Middle Ages were or non-existant or well hidden. Of course D&D settings are politheistic and not monotheistic, but the religious sense should be the same. Then one can say "Barovians are atheists" which is not wholly true, they just distrust organized religions, as they distrust Count Strahd XI and its own institutions. Areas like Dementlieu, more englightned (and more inspired to that 1650 limit we set) have of course a religious sense more similar to that of post-Renaissance Europe, and moving towards the big and traumatic change of French Revolution: remember, Louis XIV was named "Sun King" because he believed in a direct anointment of the King by Christ and God, but a century later, with the waves of a more rationalistic mindset, the same Frenchmen reacted to that.
In conclusion, playing someone involved in religion, being a cleric, a paladin, or a member of a faction, aside the specific dogmas of the individual deity, should try to get the "middle ages" mindset. It is always possible developing, in a dynamic way, a different thought, according to what happens in game, according to the character development, etc, but the main inspiration of factions like the Church of Ezra is the one and only Church of the Middle Ages, where the rights of women, homosexuality vindications, equality of "races" and people, and all these things which are the -real- progress of mankind, were yet to come. There is a reason why Gothic Novel, as a literary genre, was born in a Protestant country (England) and having the main setting very often in the dark Catholic countries (Italy and Spain): the Church in Middle Ages was the real "Dark Power" in all Europe.