There's a lot of ongoing debate as to the extent to which Anglo-Saxon Christianity at a popular level took hold, but this centres largely around elements of folkloric elements like myths, mythic creatures, 'magic' and folk medicine more than it does an active repudiation of Christian beliefs. While it's not unfeasible that there might have been isolated hold outs of Paganism in remote corners of England, by 1066, England had been Christian for over 400 years, and Anglo-Saxon Christianity had enjoyed a long reputation for its particular passion and fervour. English pilgrims to Rome were so common that an English Quarter existed there, and Alfred's '9th Century Renaissance' was marked by the a literacy drive and the dissemination of the Bible in English. There were vast numbers of English local saints, and indeed one of the main theological issues faced by the Normans post-Conquest was actually in culling the number of English saints and standardising them to an extent that was nationally practicable. English coinage from the ninth century onwards is marked by its religious design motifs and occasionally incorporated pictoral designs on a religious theme. The Conquest itself had been predicated by the death of Edward the Confessor, who was celebrated for his piety and the construction of Westminster Abbey.

As to the ethnicity question, I've answered that before here, and the answer, broadly speaking, is that while the English were perhaps only about 1/3 actually Anglo-Saxon, culturally they were far more homogenised.