I'd like to voice an opinion here, perhaps even correct some stuff :
First of all, Saxons and Norse(or "Danes", as the group was called back then, despite the region of origin) were from the same root stock of Germanics, but the Saxons you(Nightandshapedude) refer to, the ones that conquered Britain and assimilated the earlier population of Romano-British and Gaels, were by the time that the Danish incursions began(8th century, with Lindisfarne 711) a very different blend of people. Essentially, the cultural synchretism displayed by Anglo-Saxons was complete enough that by the time Danes arrived, the languages had branched off each other completely, cultures had nothing in common when compared to Jutes and Saxcis of the 5th century, etc. True, once the Danelaw was set in and cultural exchange began, borrowing and phonemic change in languages, and constant intermarriages and land deeds in the realms helped the two cultures to blend together. Then again, it was the Danes that got assimilated, not the Anglo-Saxons.
Anyway, it really didn't matter by the time that idiot William got mixed in it.
Second thing, Christianity's effect on Medieval Europe was two-fold: It was a major force both culturally and influentially. The church, or rather the monastic orders, had worked as shelters of Antiquity. They were the only place, despite several renaissances throughout periods(check for instance the Carolingian renaissance) and courts, that still cultivated written word and actual learning, while the rest of Europe(with the exception of perhaps Byzantium and it's "colonies" like Venice) was pretty happy going gun-ho over whatever plant of land or un-converted tribe was hot back then. Like a culture trips actually, just with twohanders and hauberks. It's true that you really didn't get access to the knowledge without backing or a foot inside an order, but it's not like there was much interest for people anyhow, they were too busy trying to not get killed or eaten by diseases/witches/whatever. However, without convents and monasteries, we wouldn't have medical schools, or libraries or indeed universities, they were the root of learning(once things got a bit more settled and Europe wasn't burning), here in the hinterlands of Eurasia.
Cultural depots were one thing, the other wasn't so photogenic: Christianity was an easy banner to huddle under. Just like today, people got mad with religion and alcohol and they usually had some kind of armaments. And they often appeared in massive hordes. It's an interesting thought however, that sword-conversion wasn't started by the Church initially. At the end of Rome, the Empire had practiced a policy of anything-goes and Christianity wasn't preached with swords, it crept gradually into conquered regions, brought in by officers and soldiers alike. Later on, I think it was Charles the Great that started to forcefeed the faith, started with the baptism of thousands of Sax tribesmen held at sword-end. Awful business that, but Charles understood how ideologies could band people together. He wasn't even a devout himself. In any case, medieval conversion was a relatively peaceful matter, in the early periods, when the church wasn't centralized yet and tribal chiefs could baptize their whole realms with just their word. Similarly, the first missions were done by groups of unarmed(unless you call spades such) monks from Ireland and Scotland, into Frankish Europe and Norway.
Of course, once Europe started to get borders in place, religion got into politics, which were mostly about succession and wars back then, and suddenly Rome had armies and nothing much to do except start to bust up heretics. Because priests, and especially popes, are people as well. People, who had got their hands in Iberian gold and smelt the heady scent of relics Averroes and Avicenna unearthed.
Sorry for the topic devolution, I'll go babble somewhere else.