While Norse settlers were beginning to move to the British Isles in larger numbers, were there any religious differences between native Celtic or British (I don’t know the proper terminology to distinguish native Britons that weren’t Catholic and the Catholic Anglo-Saxon) pagans and Norse pagans? Did this enmity rival the Anglo-Saxon Catholic and Norse pagan tensions? Did these tensions, if they existed, stem from differences in their religion or something else?
The State of Irish Christianity and Paganism
I think an issue you might be running up against in answering this question is an issue of time frame. While the Celtic Paganism certainly existed, by the 8th century it had been reduced greatly, replaced by Christianity. The Romans, who occupied the Isles from the 1st-5th centuries introduced the practices to Britain, where Christianity quickly adapted to the pagan traditions of the native inhabitants (as it often did in its initial spread). Ireland, the largest Celtic territory that remained untouched by the Romans, experienced some of the socio-economic turmoil as a result of Christianity from the 5th century onward. By the early 7th century the church had succeeded in relegating Irish druids to irrelevancy, while the filidh, masters of traditional learning, operated in easy harmony with their clerical counterparts, contriving at the same time to retain a considerable part of their pre-Christian tradition, social status, and privilege. Like in England and later in the conversion of Scandinavia, Christianity was not always an easy sell, but allowing individuals to maintain much of the status that they had held previously allowed for an easier conversion.
In the following centuries, Irish Christianity sought to cleanse itself of its pagan past. Cormac's Glossary (c. 900 CE) recounts that St. Patrick banished those mantic rites of the filidh that involved offerings to "demons", and that the church took particular pains to stamp out animal sacrifice and other rituals that fundamentally went against Christian teaching. What survived of ancient ritual practice tended to be related to filidhecht, the traditional repertoire of the filidh, or to the central institution of sacral kingship. A good example is the pervasive and persistent concept of the heriogamy (sacred marriage) of the king with the goddess of sovereignty: the sexual union, or banais ríghi ("wedding of kingship"), which constituted the core of the royal inauguration, seems to have been purged from the ritual at an early date through ecclesiastical influence, but it remains at least implicit, and often quite explicit, for many centuries in the literary tradition.
This is all to say that at the peak of the Viking age, the idea of pure Irish paganism was one of the past. However, Vikings and the Irish still came into frequent conflict. This was due to the very nature of the Viking age and the violence that came with the constant fluctuation of territory between the various tribes of both the Isles and of the Scandinavian raiders. However, what the modern reader may find interesting is that more recent studies of Irish battle records reveal that the pure Irish vs. Viking conflict might not have been as black and white as we may think. The best example of this is the Battle of Clontarf, a famous conflict in 1014 between the Norsemen and the Irish that is traditionally heralded as the end of the Viking invasions of Ireland. The next analysis, while slightly tangential, I believe you will find interesting as it explains some of the nature of conflict in Ireland during the Viking age and might address your last question regarding tensions between the two sides (and very conveniently something I have written a few articles about!).
Context for the Battle
The turn of the millennium was a time of civil strife in Ireland, with the consolidation of kingdoms and the growing power of individual dynasties causing ever more friction. While the reality is far more complicated, the essentials of the battle boil down to six main parties. Brian Boru was an upstart king from the County Clare, a small part of Munster. Brain Boru was the first man to end the reign of the powerful Ui Neills, first dividing the country and completely dominating. Brian was allied with the men of Munster, as well as the Connachta at the Battle of Clontarf. He was also accompanied by Máel Sechnaill, former leader of a faction of the Ui Neills and high king of Ireland. Counter to Brian’s alliance was Sigtrygg, a man of both Irish and Norse descent, who had connections with his family in the North. Alongside Sigtrygg stood men from Dublin as well as Leinster. In this scenario, it is the side of Sigtrygg that is frequently regarded as the “Viking” side, but it is clear that Sigtrygg was not alone in his resistance against Brain. Ultimately, the Battle of Clontarf led to the severe handicapping of Sigtrygg's power in Dublin. BWhile Brian Boru was killed in the battle, and Sigtrygg remained alive, the battle led to a shift of the power dynamic in favor of Brian’s side, leading many to tote the battle as the ultimate defeat of “others” versus the Irish. However, analysis of the most comprehensive primary source text Cogadh Gaedhel re Gallaibh, has made it clear that the battle was not so clear cut.
The Cogadh Gaedhel re Gallaibh, along with the Annals of Ulster are the closest examples of primary source documents from the Viking age in Ireland. The Cogadh Gaedhel re Gallaibh was composed roughly 100 years following the Battle of Clontarf. It is widely perceived as a propagandistic text, highlighting the victories of Biran Boru and his bloodline, but nevertheless deemed historically accurate. While the exact nature of the events that occurred might be tainted by the political ideology of the redactor, the historical events nonetheless likely occurred.
Network analysis of the Viking Age in Ireland- A Comprehensive and Mathematical View
Reference Figure here: https://imgur.com/a/XZI6JR6
Through a meta analysis of the names and interactions of the characters in the Cogadh, A recent paper titled "Network analysis of the Viking Age in Ireland as portrayed in Cogadh Gaedhel re Gallaibh" by Yose et. al. have been able to provide the most comprehensive view of the nature of the Battle of Clontarf to date. Yose et. al.’s landmark paper analyzed the names and relationships of all characters listed in the Cogadh. Following this, they were able to categorize the identities of the characters into “Viking”, “Irish” or “Other”, and evaluate each relationship as positive or negative. The complete network can be seen in fig. 1, with green nodes representing the Irish, purple nodes representing the Vikings and brown nodes representing other characters. Using this system, they were able to define the Battle of Clontarf with a p value of -.32, with -1 being a purely international conflict, +1 being a purely intranational conflict. This moderate value shows that while the battle may have tended toward a more international conflict it was likely a hybrid between the two extremes rather than a clear cut overthrow of the Norse Vikings, as is frequently portrayed. Yose. et. al. are quick to note the shortcomings of their study, noting that often the simplicity of their categories can limit accuracy. For example, Sigtrygg, who had both Irish and Viking parents, was defined as solely Viking. The accuracy of this examination is also limited by the document as well as the categorizing of the interactions between characters, as the record of how two individuals interacted was recorded 100 years later, and may not be entirely accurate. All this said, it is clear that in the largest examination of the Battle of Clontarf to date there is evidence for nuance in the argument between a completely international versus intranational conflict.
Why does this matter?
The fundamental misunderstandings and mischaracterizations of Vikings and Norsemen during the Viking Era is caused by a great series of these assumptions pitting the Vikings against those that they interacted with. The Battle of Clontarf is widely regarded as a international conflict, with the Irish hero Brian Boru sweeping in to finally liberate the Irish people from their violent and heathen overlords. This myth, perpetuated over time, and combined with a multitude of other events has led to a fundamental misunderstanding of Norsemen during the Viking Age.
Read the Full Paper Here: https://royalsocietypublishing.org/doi/full/10.1098/rsos.171024
Read about Cormac here: https://archive.org/details/threeirishglossa00cormuoft/page/lxxii/mode/2up
“The Viking Diaspora.” The Vikings, by Sæbjørg Walaker Nordeide and Kevin J. Edwards, Arc Humanities Press, Leeds, 2019, pp. 47–102. JSTOR, www.jstor.org/stable/j.ctvmd849f.7. Accessed 1 Sept. 2020.
Binchy, D. (1968). St. Patrick's 'First Synod'. Studia Hibernica, (8), 49-59. Retrieved September 1, 2020, from http://www.jstor.org/stable/20495893
Macalister, R. A. S. “Celtic Ireland.” The Irish Monthly, vol. 47, no. 551, 1919, pp. 235–250. JSTOR, www.jstor.org/stable/20505292. Accessed 1 Sept. 2020.