Neocatholic Church grew during the long and hard years of XXI and XXII century, years of unprecedented disasters and wars on scale previously unimaginable. Years during which many people, disillusioned with mundane powers of the world, started searching for something other they can rely on. Something stable in a world permanently changing.
When United States nearly collapsed after Yellowstone exploded, it were the various religious organisations that formed majority of relief groups, with government actually giving them resources and military support, weakened to the point of not being able to achieve it by itself. When Western Europe collapsed into totalitarianism and ethnic cleansings after the Islamic War, it was the Catholic Church that opposed this changes the loudest, with many of its adherents dying martyr's death. After all world powers collapsed in the aftermath of Third World War, it were the religious groups that formed the core of the attempts to send relief to decimated areas of the world.
As people become more and more disillusioned with the world they seen in front of themselves – one ridden with wars both civil and international, epidemies, famine and natural disasters – they started searching for the answers in religion, beginning the period of resurgence of religion throughout the world. Not only Christianity benefitted from it, but in fact all religions, including many new ones made by people who were dissatisfied with already existing faiths.
As such, when the Outer Colonies were settled, surprisingly many of the colonists were religious. Of course, equally as many were atheists, but those who actually believed were many... and their faith was strong. It was also the faith that changed Fourth World War into many years long stalemate, as technologically superior armies of Federation found themselves incapable of defeating Nationalists, who, however weaken in terms of equipment, could field entire armies of zealots, fighting with fanatical devotion. To win, Federation was forced to use atomic weaponry to cleanse holdouts of Nationalist, changing many areas of Earth into postatomic wastelands.
For the faithful in Outer Colonies it was a shock. They didn't leave Earth so far ago to not remember it at all, there were many of them who were born on it... mostly in places that underwent atomic cleansings. The humanity's greatest atrocity, commited on faithful by atheists. Many began to search for answers to their question in their history, only to find even more abominable atheist regimes - like Third Reich, USSR, People's Republic of China or even Revolutionary France - using genocidal methods to purge the world of 'outdated' ideas like religion.
Religions that survived the Fourth World War went radical in their hatred for atheism. Not to atheists, at least most of them, but atheism as a belief was condemned as abominable extremist doctrine. Actions of countries like The Technocracy
that went genocidal during Unification Wars – while being atheist – only worsened the situation. Even many generally secular states (like european colonies of New Europe) begin switching their mental sculpts to artificially created forms of deism or theistic agnosticism, under the pressure of local religious organizations. Many weaker atheist states fallen to the Faithful (of myriad of faiths) during the Unification Wars, their atheism serving as casus belli, the wars considered prevention of eventual genocide that began to be associated with atheism.
Finally Unification Wars ended, and the Galaxy stabilized politically. With restored communication between sectors, new attrocities of atheism (those of religious states thought to be condemned 'exceptions') were discovered as well as Terran Federation, abominable bastard of Fourth World War, one responsible for countless deaths among the believers of all religions. Many religions – splintered during the colonization – began to attempt reunification, hoping to better combat new threats.
One of such attempts was made by variety of Christian churches that assembled upon planet of New Jerusalem - a hideout, to which many Faithful from Earth's Jerusalem fled taking many most holy relics with them before the atomic cleansings, in a long and ardurous journey that was thought as a sign of God's favour. After bishop of Rome (on exile) joined them, the combined authority of the head of strongest Christian denomination and jerusalemites was enough to organize an ecumenical Council of faithful.
The Council deliberated for four months, nearly perpetually. With hundreds of clergy and secular having to start from actually organizing themselves into a working council. Soon first breakouts occured, with many surviving denominations - like Jehova's Witness or Mormonism - decided to not be Christian due to lack of acceptance of Jesus as a God. The rest worked relentlesly, slowly but surely closing the gaps between them, accepting the most basic doctrines of the new, united Church, with a common enemy of extremist groups working like a great mean of unification.
Finally, the Catholic Church was created, one finally truly common. With dozens of different theologies and liturgies, but with several pillars that held entirety together - including the staunch opposition to extremist ideologies (including atheism as a whole, a clear sign of the time, but also fascism, communism, socialism, and anarchism), the need for the religion to be represented in politics to protect the Faithful, the belief in godhood of Jesus Christ, lack of acceptance for slavery, geneengineering of sentient species, cerebral implants with surveillance capabilities, religious or racial intolerance, abortion, euthanasia, certain forms of anticonception, orbital bombardment of civilian targets, forcible mental resculpting, destroying environment of habitable planets and sentient AI creation.
The unity, achieved with great efforts, collapsed unfortunately very quickly, for in 2265 (after merely fifteen years) were many sects seceeded following the influx of plants
and doctrinal question of existence of soul among aliens. The schism occured following the decision made on Fourth Vatican Council - with Neocatholic Church deciding to accept divine origin of all creatures capable of understanding the Gospel, together the need for the Church to share the gift of salvation with all sort of sentient life. Those that disagreed, seceeded, creating second Neocatholic Church (officially, practically it is called Paleocatholic Church due to it 'sticking' to old ways), that soon splintered further, into many local groups.