Origins and beliefs
They come from the Rivenese who witnessed the efforts by Atrus and Katran against Gehn. Two Rivenese were present at their confrontation at the Star Fissure. They understood little of what they were seeing, but they realised that Gehn was no god but an impostor, and the strangers had defeated him, by trapping him on Riven.
Having their land destroyed and being oppressed, out of ignorance they found beliefs to cling to. They came to believe that Atrus was a true god, and had stripped Gehn of his power. Katran, who had been always a "spiritual misfit" was his chosen wife and therefore also divine. Other beliefs that evolved had to do with Katran would overthrow Gehn, or that she will bring them to paradise.
They revered the Rivenese daggers that appeared during the escape from Riven, specifically the one that fell at one end of the Allatwan. Without knowing that it was katran who wrote them into the Age, they developed their own mythical explanation regarding its nature and origins. They adopted its shape as their sacred symbol, representing their doctrine, and Katran. To deface this symbol is sacrilege.
They refuse to be seen by those not of them, and during their sorties they wear frightening masks and costumes, getting pleasure when the villagers take them for evil spirits or ghosts.
In the early days, the Moiety sought an escape from Riven and briefly pursued the idea of reopening the fissure which Gehn had sealed. They stole the combination to the portal window, but ultimately, they decided against opening it.
During one of their operations, one of them managed to steal one of Gehn's partially written test books which he intended to destroy.
Over the years, as Gehn's power became greater, so grew the Moiety's numbers. They became more adept at hiding themselves and found a home in a complex network of caves on the Jungle Island that Gehn had not discovered. For the most part, they had completely severed their relationship with any of the Rivenese that chose against joining them and remained on the surface. From there they interfered with acts of sabotage against Gehn's constructions, or by stealing food from the villagers.
It was during one of these forays that they rescued Katran from Gehn's guard when she first appeared again to Riven. They took her to their caves and there she found out their views about her, and their expectations. She felt uneasy feeling special among them, and although she attempted to dispel some of their superstitions, their beliefs proved unbending, as they didnt expect to hear such words from her. From them she also learned the news about Riven and Gehn's whereabouts. 
Catherine was able to modify the book hey thad stolen and turned it into a workable age. Catherine made them discover the combination of the domes and also steal a linking book to Riven so that they could be transferred to the Moiety Age. Once the Moietor-Esk took notice that Gehn operated his domes, Katran used one to link to the Moiety Age and returned providing them with book windows.
It seems that under Katran's leadership, the rebels became more sophisticated and bold and increased their acts of vandalism and theft. Taking advantage of their common superstitions, they renewed their campaign to intimidate the villagers into joining them. They began leaving their daggers as a signature, mostly on the south side of the village, where people were "disappearing". Gehn found that the daggers contain elements that don't exist on the islands (apparently made by material from their secret Age).
One night a squad of Rivenese Maintainers apprehended a lone rebel scout and obtained a book window from him, which Gehn studied.
The Moiety had installed several wooden spheres around the island, associated with a Rivenese animal and a D'ni number, being the key to their linking book. Gehn had noticed those objects but didn't know their purpose.
When the Stranger linked to Riven, a Moiety rebel darted Gehn's guard once more and freed the Stranger, but not before collecting the Prison Book from the guard, which the Stranger had brought with him. When the Stranger found his way to Tay, he was captured by two Moiety guards and brought to a closed quarters. There Nelah provided him with the Trap Book they had stolen from him, as well as a linking book back to Riven.
The Stranger used information gathered by Catherine and the Moiety and opened the fissure, hastening the destruction of Riven. Shortly before the destruction the Moiety were oined by the rest of the Rivenese, as Catherine managed to lead them to the Rebel Age where they apparenty in order to rescue them.