Prior to the war, The Church of Jesus Christ of Latter-Day Saints, otherwise known as the Mormons, was a rather bizarre pseudo-Christian religion based out of Salt Lake City, Utah. They were one of the few organized groups to survive the apocalypse reasonably intact, though changed significantly from their prewar form.
Prewar history
The Mormon religion was founded by a man named Joseph Smith in the 1830s after he claimed to have found a book (inscribed in Egyptian heiroglyphs on golden plates) written by ancient Isreali migrants to the New World as a chronicle of their history. The accuracy of this claim is open for debate, as fewer than a dozen people ever claimed to have seen the plates, all of them high-ranking church officials, and the plates themselves have never been found. It was also never explained why people of Hebrew descent would write their books in Egyptian.
Despite being persecuted pretty much everywhere they went (and nearly started a second Civil War on two separate occasions), the Mormon faith grew and prospered over time. Eventually, they settled in Utah, establishing the permanent headquarters of their faith in Salt Lake City, where they erected an extravagant temple. They began an aggressive campaign to spread their faith worldwide, including essentially mandatory two-year periods of missionary work for all young men (ages 18-20) in the church. At the time of the apocalypse, they were the fastest-growing religion, in terms of membership, on the planet.
During the War
Salt Lake City, the church’s global headquarters, is also the capital of the state of Utah, and as such was a designated target for nuclear attack. It, along with most of the church leadership - the Prophet, the Quorum of the Twelve Apostles, and most of the Quorum of the Seventy - was utterly destroyed. In the brief period between the start of the attacks and the total loss of all global telecommunications, the last surviving members of the Seventy announced that the headquarters of the church had been officially relocated to Nauvoo, Illinois; none of the Mormons in the areas that would eventually be known as New Nevada and the Arizona Deadlands ever heard from them again.
The Mormon faith was widespread enough in the Western United States and Latin America that a disproportionately high number of its practitioners were still alive when the bombs finally stopped falling, though many died in the period of anarchy and destruction that followed. Those that remained tended to cluster together in exclusive enclaves for mutual protection; over time many of these enclaves became heavily fortified, self-sufficient settlements.
Postwar
The Mormon faith lacks much of the organization and bureaucracy it once had - although there is, in theory, still a leader with absolute authority and the lesser councils to advise him, no one has heard from the high leadership of the Church in well over a century, and none of the expeditions sent to reestablish contact with Nauvoo have ever returned. This has led to something of a schism in the Church - there are at least a dozen subfactions in the New Nevada and Arizona Deadlands regions alone, each with a leader or group of leaders who claim that they alone represent the true intentions of God, Christ, and whoever the hell the current worldly leaders are; at least one even claims to be in communication with Nauvoo, though he has provided no proof of this claim.
The largest known faction is headquartered in what was once Provo, Utah, and boasts well over three thousand members, at least four hundred of whom are organized into a full-time military force; they control practically no territory, excepting the town itself and the farms surrounding it, but what they do control is quite well defended. Most of the smaller factions have membership rolls numbering in the hundreds, with two having a thousand or more and one particularly isolationist group having fewer than seventy members, most of them old men.
In terms of philosophy and doctrine, the modern church is quite similar to its predecessor. The average Mormon is not particularly fond of people of African descent, Native Americans, Asians, or anyone with /any/ kind of mutation or cybernetic modification whatsoever; someone who belongs to any one of these groups is often denied membership in the priesthood, or even restricted from joining the church entirely. Mormons shun alcohol, tobacco, recreational drugs of any kind, profanity, pornography, and most other traditional vices such as adultery. They embrace collectivization, believing that all members of a community must work together as one single entity to function properly; as such, personal property is often shared amongst community members, and anyone who refuses to share is often shunned and excommunicated. Women are expected to look after the house and birth children; they are denied membership in the priesthood and possess no authority in the church. Unlike the old church, most modern Mormons are rather isolationist and borderline xenophobic, deliberately avoiding contact with the outside world as much as possible.
The Mormon church has always been governed, at least at the local level, by laymen - the bishop and other positions of authority are elected by a popular vote of the congregation, with terms lasting anywhere from six months to four years. Any member is permitted to speak in front of the congregation; indeed, members are often /required/ to give sermons; the speakers for a given Sunday are selected at random the week before.