'Abd ar-Rahman hasn't always been the stern moralist priest we know and fear today. As a youth he was known as M'hand and plied the not-so-honourable trade of wrecker, luring merchant ships onto reefs around his native island of Lzaier, on a remote prime world. One day however, as he was exploring the wreck of a rich ship from the north, he heard the moans of an old man. He approached stealthily and unsheathed his djambiya, but as he was about to slice the throat of the old man, their gazes met. M'hand saw such goodness that he just dropped the blade and kneeled down in front of the old man.
From that day on, he acted as guide, bodyguard and disciple to the old 'alim. Under his guidance, he soon learnt how to read and write (for he was a bright pupil) and he acquired much holy knowledge about the Loregiver and Enlightenment.
The years passed, and M'hand finally became an acclaimed scholar of the Loregiver, and a much revered moralist priest. He took on a new name, 'abd ar-Rahman, and started wandering his world to bring Enlightenment to those in the need. He gained many converts and proselytes to his cult, and eventually gained the title of Imam. As such, he was now always accompanied by a strong following of pilgrims, acolytes and farisan.
One day, as they'd landed on an unknown island south of the known lands, Imam 'abd ar-Rahman spotted a cave entrance which seemed to have been made by mortal hands. He entered the cave with a handful of farisan, and they soon found a set of stairs going down. The stairs led them to an old, bronze portal that they managed to open. Of course, the portal was just that -- a portal -- and Imam 'abd ar-Rahman was unknowingly holding its key (a burning bit of wood) in his left hand. He and his farisan entered the portal and were transported to Sigil.
and you'll lower everyone else's self esteem."
Imagine the bewilderment of a group of pious men suddenly finding themselves in the midst of a stinking, motley crowd of men of dubious aspect and scantily clad women! They immediately turned back and tried to enter the portal again, but it was raining in Sigil that day, and the torch was put out.
Nevertheless, Imam 'abd ar-Rahman managed to get accustomed to the Sigilian ways and became a factor of the Harmonium (whose philosophy best suited his moralistic views). Eventually, he managed to get assigned to the Outer Planes (for he hated Sigil and wanted to leave the Cage) and held various appointments on Arcadia and Mount Celestia, where he met Formigoni, a fellow Hardhead and prime; they became close friends.
Imam 'abd ar-Rahman and Formigoni had a feeling the Harmonium was too soft on trespassers of the laws, and especially on sinners. They soon formed a small 'fraction' of the Harmonium whose aim was to track down sinners and punish them. Formigoni even located a proper place for punishment on Baator, and they shared their task: Imam 'abd ar-Rahman was to find the sinners and judge them, and Formigoni was to carry out the punishment on Baator. Things went along smoothly for some time, but Imam 'abd ar-Rahan noticed that his friend was becoming more and more obsessed with the way sinners got punished and not the reason why they were being punished. Eventually, their 'fraction' split and Formigoni's followers became an evil sect known as the Punishers. On the other hand, 'abd ar-Rahman's followers stayed within the Harmonium, but they've had ever less interaction with fellow Hardheads since the fraction's split. Today, they're known as the Inquisition, and are based on Buxenus.
The Inquisition (they also call themselves: The Enlightened) have a mission: To track down sinners, to bring them to Buxenus to Imam 'abd ar-Rahman who judges them for their sins. The sinners are then handed over to fellow hardheads when they're deemed "recoverable" or given to the Red Death for punishment. Most people in the Harmonium's 'reeducation camps' were arrested by the Enlightened, but since these camps are slowly being taken over by more by-the-book Hardheads, the Inquisition is looking again for new headquarters and for a new playground: The Prime Material Plane.
Well, it seems that Imam 'abd ar-Rahman's getting sterner with age, and he has decided that the Inquisition shall focus on Primes from now on. He is training recruits to set up secret bases on any prime world they can have access to and to bring enlightenment to its inhabitants - ie: to seek out the sinners and punish them.
That is the current situation. Given the vastness of this new task, the Inquisition could just disappear. Equally, they might well become a major force within the Harmonium or even break away from their mother faction and become a sect centred on the Prime.