There was once a time before 664 where Ionan Christian beliefs dominated Northumbrian Christianity, nearly upended the Gregorian mission, and rivaled papal power in the British Isles.
I think it's a mistake to distinguish a Ionan Christianity to a Pontifical Christianity : at this point, most Western Churches differed by several pastoral, ritual and liturgical details which differed more or less importantly from the Roman practices, for exemple what went to be called the Mozarab or Visigothic Rite.
Maybe more significantly, the synodal organisation of churches, while definitely acknowledging the Roman, pontifical, supremacy were set up by the royal (or ducal in some case) figures, in Britain as in the mainland.
The differences were less a rivality between abbots and the Pope (both being far too distant to really oppose to each other), but a rivality between tenents of traditional rites and tenents of the first waves of standardisation of practices among British and Irish clergy. You could say "Ionists" and "Romanists" if you will, a rivality that a recently converted Oswiu (I don't think speaking of Northumbrian Christianity is that accurate : it was still essentially a "church-in-being", so to speak), had to resolve in an early medieval conception of power (as said, which covered synodal organisation) all the more necessary as Oswiu had obtained the hegemony over most of Anglo-Saxon England. Charlemagne won't do anything else in his time.
From what I have at hand myself, most of the differences at hand were quite minor and already on the path being resolved : an english-speaking historian apparently called the whole thing "a triumphant push against an open door", as Ionan traditions were challenged even in Ireland : Oswiu eventually replaced Britto-Gaelic clerics, in order to replace other Britto-Gaelic clerics, and not from mainland (altough several of these clerics, as Ronan, did studied in Gaul and Italy), the aformentioned Romanists against Traditionalists.
Now, the historiographical point is less about some really minor points, than structure and organisation : basically about who would get to have the upper hand on ecclesiastical lead.
Ionan and Irish churches were more centered on monachial and abbatial structures (while episcopalian weren't absent, but secondary); while others (and specifically in southern Britain, trough Frankish influence) put the stress on bishops and compatibility of practices.
On this last part, the relation between royal power and synodal power is worth being noted, as in virtually all the continental kingdoms, you had a situation that evolved from Late Roman's : the king (inheriting imperium) more or less presiding over an episcopal assembly (of course it evolved from this : Councils of Toledo points how, but it didn't diverged radically at this point).
Having the king presiding over such synod, and getting to make the decision, was already (IMO) pointing how Ionian's positions didn't exactly began as the winning side, especially when remembering that Augustine had to battle with Britto-Romans waiting for a general assembly to decide the matter.
Romanists tendencies were already present in Northumbrian courts, Oswiu's son that ruled Deira already enacted pro-Romanists decisions in the sub-kingdom which probably forced his father to call a synod. Maybe as much importantly, queen Eanfeld was Kentish (Kent was one of the first converted Anglo-Saxon kingdom, and right from the beggining abiding by a Romanist tendency, due to Frankish presence if not suzerainty).
While Iona itself was divided about what to follow, Anglo-Saxons kingdoms abided more and more trough Romanist lines : let's be really clear, it doesn't mean the huge Ionan influence disappeared, at the contrary it remained really strong and created an original Anglo-Saxon Christianity. But this influence exerced itself on a different ground.
While the synod wasn't that a world-shattering event (it had virtually zero consequences on the continent) and didn't decided the matter of Christianity in early medieval Britain, it was still an important rupture as a tip on the balance, part of a wider process : after all, Bede points that most of the organisation left by Colman remained in place for years after his departure, and most of native liturgic and religious structures remained in place up to Norman conquest and well after (Davidian revolution, conquest of Wales, etc.)
Eventually, it's more about how much mix between Romanist and Traditionalist beliefs and practices you'd end up with, less than how to prevent it especially with this PoD.
https://en.wikipedia.org/wiki/Celtic_Christianity
https://en.wikipedia.org/wiki/Synod_of_Whitby
