The conversion seems to have been quite rapid. I think even before Alfred’s descendents had fully reconquered England back (or the Danelaw), the Danish settlers had largely become Christian.

In Anglo-Saxon England, within the space of a single generation, pagan warriors had become Christian farmers. Christian burial was rapidly adopted (Wilson 1967), many choosing to be buried in churchyards (Graham-Campbell 1980). “By the tenth century their ferocious leaders were commissioning stone crosses and establishing private chapels on their new estates.”

The Evidence... all points to wide acceptance of the new faith already by the end of the 9th century. In the first decade of the 10th century the Danes can still be classed “pagans” by their enemies, but this is the last indication of any continuation of heathen religion (Whitelock 1941, xx).

Those Vikings who, after the late ninth-century partitions of land in East Anglia, Northumbria, and Mercia, settled in the area later known as the Danelaw, were amongst the first Scandinavians to adopt Christianity. They were Christian at least two or three generations before Harold Bluetooth’s claim to the conversion of Denmark (Roesdahl 1997) . The rapid conversion of Scandinavian settlers, so we are led to believe, demonstrates the weakness of their own pagan religions in the face of an all-embracing Christianity, and provides another example of their eagerness to become assimilated.

Danes were not violently removed. If you mean St. Brice's Day massacre then that was mostly confined to Danish mercenaries who had recently arrived in England‘s shores to work for the English King, not Danes who had been living in England for over a century. Essentially, the religion of Danish settlers wasn’t much of an issue even by the time the Danelaw was reconquered by the Saxons since they had already become Christianised.