Although someone else will be able to provide a shorter-term context for your question, I can say that Christianity in Ireland and Scotland in the early Middle Ages was quite different from the Roman Catholicism accepted in England.
The 'Culdees' provide one example of how removed Celtic people often were from the Roman Church, these being individuals who lived an eremitic lifestyle, beyond the reaches of society. This practice had occurred in the Middle East since practically the dawn of Christianity and began too in Ireland in the 7th century and continued until Ireland was brought into the Roman fold in the 12th century. There are no less than 9 areas in Ireland where it was common for young men to remove themselves from established settlements and live a holy life of prayer in almost complete seclusion. Like their Middle Eastern counterparts, they deliberately attempted to find the most wild and deserted places - bogs, forests, crags, even islands off the Atlantic coast of Ireland. Removing themselves from society to form a stronger link with God, they presented a potential challenge to lay powers, who themselves claimed to be representatives of God.
Celtic monasticism openly looked to the East for its inspiration, as shown in the words of an 8th century liturgical text from Bangor Monastery that once stood in modern-day Northern Ireland:
This house full of delight, Is built on the rock, And indeed the true vine, Transplanted from Egypt.
We can also look at the 'seven monks of Egypt in Desert Uilaig,' recorded in the 9th century by Oengus the Culdee, an Irish monastic bishop. It was claimed that just invoking the names of these monks from the East was enough to ward away injury.
It becomes apparent, therefore, that many Irish and Scots did not look to Rome for their spiritual guidance, but to the Eastern Churches, drawing direction from the people, monks and holy men from the Levant in the early Middle Ages. This early lack of conformity helps to explain why the Pope published a Bull in the 12th century to bring Ireland into the Roman Church, and by doing so, supplying Henry II of England with a 'casus belli' to invade.
In the longer term, as /u/Hollowegian has described, Ireland was pretty different from mainstream Latin Christianity (Roman Catholicism is a 16th century invention!), but when Laudibiliter was issued it was much less so. The 'Culdee' or 'Céilí Dé' movement has at its height in the seventh and eight centuries, for example!
In fact, Irish kings, in particular those who aspired to the High Kingship such as the Ui Briain/O'Brians of Munster, had, like many other kings in Western Europe in the late 11th and early 12th century taken up the cause of church reform with gusto, inspired by the reforming popes (the Ui Briain Kings of Munster exchanged several letters with both Gregory VII and Archbishop Lanfranc of Canterbury in the late 1000s on ecclesiastical matters).
By 1155, Ireland had replaced the older, monastic organisation of the church with a modern diocesan structure and had received the papal blessing and 'pallia' (ceremonial archbishops' scarves) from Rome. This was all undertaken by native kings and clergy based on ideas imported from the continent, with reformers such as Malachy of Armagh traveling to France and Rome and maintaining relationships and friendships with leading continental churchmen, such as Bernard of Clairvaux. If there were any allegations to be made against the church in Ireland diverging from mainstream norms it was in the lack of effort made to enforce clerical celibacy and the hereditary succession to church offices, but this was hardly radically different from in Europe where even around 1100 high ranking clerics were publicly arguing that clerical marriage be allowed and the battle against simony and clerical marriage dragged on for centuries.
So, in short, Ireland wasn't that different from mainstream Latin Christianity in 1155, certainly no more weird that Scottish, Scandinavian, Spanish or Central/Eastern European Christianity. However, the trope of uncivilised and barbaric Irish people was an effective tool to justify the invasion of Ireland (read Gerald of Wales' description of Ireland to find out just how wacky those allegations could be) and continued to be so right into the Early Modern Period.
Laudabiliter is more complicated though. It's easy to see it as a convenient 'causus belli' for Henry II to invade Ireland, except that Henry II never did invade Ireland and the bull was issued 15 years before any organised English force came to Ireland. When they did, in 1169, it was as mercenaries and allies to a down-on-his-luck Irish king and it was only after his death that the English, led by Richard 'Strongbow' de Clare seized his kingdom and threatened (inplicitly) to form an independent Anglo-Norman kingdom in Leinster. It was only THEN that Henry II stepped in to stop such a potential threat to his power from forming.
As for the papal Bull, the best explaination I've heard is that there was a faction in Henry's court in the 1150s which favoured an invasion of Ireland, for whatever reason, and they gained a bull legitimising such a potential invasion (from the only English pope ever, one might add!) but Henry, again for whatever reason, decided against the invasion. So the bull was forgotten until circumstances forced Henry to go to Ireland in 1171-2 and then was conveniently dug back out.
Sources: Sean Duffy, 'Ireland in the Middle Ages' (Good general info); Aubrey Gwynn, 'The Irish Church in the Eleventh and Twelfth Centuries' (Lots of detail on the Irish church and the reform movement in Ireland, plus Laudibiliter); Robert Bartlett, 'Gerald of Wales' (Has a detailed discussion of the 'savage Irishman' trope, its intellectual history and the motivations behind it).