This is something I have trouble understanding. Before the Norman invasion in 1168, Ireland had its own Celtic Church. Supposedly Pope Adrian IV issued the Laudabiliter papal bull in 1155 to bring the Celtic Church in line with the Roman Church and force Gregorian reforms. The island was taken as a Papal possession. Wikipedia has some harsh quotes like
The Norman invasion of Ireland thus had the backing of the Papacy. Pope Alexander III, who was Pope at the time of the invasion, ratified the Laudabiliter and gave Henry dominion over the "barbarous nation" of Ireland so that its "filthy practices" may be abolished, its Church brought into line, and that the Irish pay their tax to Rome.
You would think that throughout the centuries that this would have been imprinted as a collective memory on the Irish people. Yet, to my knowledge, the Irish clinged to Catholicism a lot. They wouldn't accept Protestant reforms under the Tudors and the Irish people's association with Catholicism goes right through the penal laws all the way to the war of independence.
What gives? Why would these people defend so vehemently the very organisation that betrayed them? Why wasn't there a schism of the Celtic Church from the Catholic Church? That seems more like the Irish people's first and true Christian organisation.
There wasn't really any such thing as a "Celtic Church". What we refer to as "Celtic Christianity" was not a separate church or organisation but rather a set of distinctive traditions and practices common to the Catholic Church of Ireland and other "Celtic" lands e.g. a different way of calculating the date of Easter and different penitential practices. 12th-century practitioners of these traditions would not have seen themselves as members of a different chrch opposed to that existing the rest of Europe which could potentially break off relations with their their co-religionists because of the decision to issue Laudabiliter.
See "The Myth of the Celtic Church" in "The Early Church in Wales and the West" http://books.google.ie/books?id=MZLYAAAAMAAJ&q=%22myth+of+the+celtic+church%22+early+church+in+wales+and+the+west&dq=%22myth+of+the+celtic+church%22+early+church+in+wales+and+the+west&hl=en&sa=X&ei=jz1JU6OgIufX7Ab5vIHABw&ved=0CDAQ6AEwAA
There has also actually been a good bit of controversy historically about the actual authenticity and meaning of Laudabiliter. http://www.historyireland.com/early-modern-history-1500-1700/laudabiliter-a-new-interpretation-by-professor-anne-duggan/
An interesting document in this context is the "Remonstrance" sent to Pope John XXII in 1317 by Irish kings and chiefs led by Domhnall Ó Néill which basically protests against Laudabiliter and asks John to revoke it and recognise Edward Bruce as king of Ireland.
"Pope Adrian, your predecessor, an Englishman not so much by birth as by feeling and character, did in fact, but unfairly, confer upon that same Henry (whom for his said offence he should rather have deprived of his own kingdom) this lordship of ours by a certain form of words, the course of justice entirely disregarded and the moral vision of that great pontiff blinded, alas! by his English proclivities. And thus, without fault of ours and without reasonable cause, he stripped us of our royal honour and gave us over to be rent by teeth more cruel than any beast's; and those of us that escaped half-alive and woefully from the deadly teeth of crafty foxes and greedy wolves were thrown by violence into a gulf of doleful slavery." Full text here http://www.ucc.ie/celt/published/T310000-001.html
You have made several assumptions in your question that I take exception with. First, there was no Celtic Church. There was Celtic (or Insular) Christianity, but there was not a central organization that formed an official Church. Celtic Christianity was fairly distinct between Provinces, Monasteries, and the leading Abbots. /u/reidit777 gives a great answer about this. Second, the Laudabiliter was, at best, a means to a political end and not the justification for England to conquer Ireland that many people make it out to be. It did not make Ireland a Papal possession: it gave Henry the Church's blessing to conquer Ireland.
Ireland was on the periphery of the early Norman Kings: it wasn't Papal urgings that finally pushed them into Ireland but the need to assert power of their own. Dermot MacMurrough, King of Leinster, invited the Earl of Pembroke (better known as Strongbow) to Ireland in order to assist MacMurrough in reclaiming power that he lost in 1167. After MacMurrough died in 1171, Strongbow claimed his lands and himself King of Leinster & Dublin. It was in response to one of his own Earls claiming a Kingship in Ireland that finally convinced Henry II to intervene in Ireland. For the sake of land and power, Ireland was doomed to English conquest with or without the Laudabiliter.
You ask why "these people defend[ed] so vehemently the very organization that betrayed them" but they really didn't defend the Catholic Church. Instead, they sought to retain their culture, which had grown from the pre-Norman Celtic Christianity into European Catholicism. They defended themselves, their culture, their beliefs, lands, livelihoods. There was not schism because there was no proper Celtic Church.