The temples you see in the screenshots belong to the cult of Mother Sophia.
It is the dominant religion with great power. The supreme body of the cult is the Holy Synod.
The dogma of the cult is described in the sacred books Revelations of Sophia and Testimony of Truth. You can read excerpts from them here:
Another book, "The Hidden Knowledge", which contains knowledge of the technologies and calculations of the date of the Great Purification, is accessible only to the highest members of the Holy Synod.
In the temples of Sophia is her statue with the face of the sun; her right hand wields lightning – the element of destruction, through which Sophia sends fires on sinners– and in the other hand a key, the symbol of access to rebirth, which is awarded to anyone who observed the commandments during life and whose soul is pure.
The bodies of the dead are burned on the two altars, the souls go out through the smoke and return to heaven – to the Mother.
Through preaching in the temples, the player can increase or decrease the number of fanatical believers, which can be recognized by the Sophia cross on their bodies. They have a strong mood bonus and tend to take pleasure in pain, but they are also more prone to conflict, and in greater numbers can start a religious pogrom which can result in the slaying of all unbelievers or agnostics in their path, including the player's lords.
The city's accepted tenets determine which actions are sinful and lower the Piety parameter, and which will raise it. For example, these can be dice, confession, and sacrifice. However, having learned new dogmas from books or from revelation (which happens to lords after a nervous breakdown or an epilepsy attack), a player can try to implement them into the culture of his settlement, making, for example, walking naked at night a godly thing.
However, each modified dogma increases the hereticism of the local culture, and the Holy Synod does not like it. At some point, it may send an army of inquisitors who will burn your Scriptorium with all the books, and try to kill all the carriers of heretical dogma, thereby resetting the religious settings to their original ones. Maybe you yourself will ask the Synod to do this if heresy goes too far (such as arms and violence becoming forbidden).
The Holy Synod does not only watch over heresy. It is governed by the five Children of Sophia, and is located within the impregnable stone castle of the Stone of Faith, where the player can send his emissaries for intrigue.
Only the Holy Synod has the ability to build stone structures, to trade through Holy Caravans, to issue gold coins and Holy Rings. Thus, it has in its hands the most powerful instruments of economic control. But this is for the greater good – someone has to prepare humanity for salvation during the Great Purification.
But we’ll talk about that another time.