One extremely interesting part of Lancer deep lore is that the Catholic Church still exists, and the implications of this are fascinating.
The existence of the Catholic Church in Lancer is evidenced by this passage from page 121 of No Room For A Wallflower Act 1:
Catholicism is such a prevalent world religion that it would almost certainly have had many adherents on all of the Ten, which meant that everywhere the Ten went, so too did Catholicism. The Ten left starting around 6000bu, and instantaneous FTL communication didn't appear until around 3200u, which means that for over 9000 years - longer than the current human historical record! - Catholic dioceses on old Earth colonies could not have maintained full communion.
There was also no contact between Earth and any of its colonies by any means (FTL or not) from 6000bu to at least 1400u, and realistically several centuries after that. 1400u is when Union on Cradle first turned its long-range communication systems back on and experienced the Third Trauma; they didn't start to send regular messages to surviving colonies until significantly after that - first contact with the Karrakin Trade Baronies didn't happen until 2800u, more than 800 years into the First Expansion Period.
This puts the earliest that the Catholic church on Cradle could possibly have had any contact with orphaned dioceses at around 8000 years. This exceeds the current lifespan of the Catholic church by more than four times.
It is reasonable to assume that in the absence of any possible contact with the Holy See on Earth, Catholic dioceses on the colony worlds would have to establish their own central authority - essentially, a series of definitionally non-competing antipopes. The realities of time, distance and differing environments would cause dogma in each separate diocese to drift.
We've already seen this happen on Earth: Irish Catholicism is notably different in character to American Catholicism, and both of those groups can pick up a phone and talk to the Pope! Meanwhile, some of the Ten went to planets hundreds of light-years away - even if you could send a question to the Holy See, by the time you got a response back, assuming your civilization endured, the cultural conditions that provoked your question would most likely be historical curiosities discussed by your distant descendants.
So imagine the nightmarish complications around 3200u onwards, during the Second Expansion Period, which is when FTL communication and travel became commonplace in the Lancer universe. This is a reasonable point to posit that the "Catholic Union" mentioned in Wallflower came into being.
Let me set the scene: the Cradle Papacy proposes, now that FTL communication is possible, to reunify the Catholic Church and return the faithful across every human world to full communion with the Holy See (SecComm was ascendant back then; this feels like the sort of One Humanity shit they'd pull). With Union's newly-built OmniNet, the Cradle Pope reaches out to the archdioceses of Karrakis, Carina, Tau Ceti, Rigel Kentaurus, Spinward Ultima…
Cradle Pope: "Blessings upon you all, from the Church of Peter the Apostle, First Bishop of Rome, in the name of the Father, the Son and the Holy Spirit."
Karrakis Pope: "Oh, hey! Which one of the Passions are you Bonded to?"
Sparri Pope: "Blessings upon you in the name of Saint Anaru, who vanquished the Beasts of God and ate their eggs."
Constellar Pope: "I have a brain implant that constantly updates the Liturgy for me!"
Bishop-Regent of Ras Shamra: "Blessings upon you in the name of Malcolm XVII, Prophet and Final Pope, who harrowed the Nightlands."
Cradle Pope: "Guys what the fuck"
The Catholic Union in 5016u must be an absolutely batshit compromise between a multitude of utterly incompatible regional dogmas that exists broadly so that these separate churches can exercise collective political authority.
… so actually, kinda like the Catholic Church has always been.