Monotheists believe in a more rigid code of ethics and morality than polytheists - they see the world in shades of "black and white" rather than shades of gray.
Repelled by the hedonism and barbarism of parts of colonial society (in particular the Virtual World), they have adopted as their mission to clean up the vices and sins of the worlds by sharing the word of their omniscient and omnipotent god. ("Pilot")
The church is headed by The Reverend Mother, who lives on Gemenon at a place called the Retreat. ("Blowback") The Conclave is a governing body which meets here. They are headed by a leader who reports directly to Mother and is her advisor. ("Unvanquished")
Soldiers of the One has a training camp located on Gemenon. In the early years of the monotheistic movement, the STO safeguarded the church. Now that the church is more established, they have become more comfortable with their polytheist neighbors. This has led them to publicly disavow the STO and to treat them poorly, such as making them live in tents in the cold instead of allowing them to reside in more comfortable rooms in the Retreat. However, regardless of their public stance on the STO, the church still relies heavily on them in secret for covert operations. ("Unvanquished") ("Here Be Dragons")
The Monotheistic Church is located between two warring factions - the polytheistic rebels on the east and the Hephaestons on the other side. Diego, one of the STO leaders, says it is a big stalemate. ("Unvanquished")