Actually, they were Jehovah’s Witnesses. There are a couple of Watchtower references toward the end of the series.
I see a few parallels between cylons and JW’s. But ultimately it doesn’t work because:
1 - JW’s are extremely anti-military and anti-military action.
2 - JW’s aren’t monotheists in the strict sense. They are one-and-a-half-theists. JW’s believe in Jehovah (God the Father), and have more-or-less adopted the Arian heresy’s view of Jesus as demi-god. (If I not mistaken they also hold Jesus to be the Archangel Michael.)