The Anglo Saxon Chronicles (a collection of manuscripts Chronicling the History of the Anglo Saxons, often covering minute detail such as ecclesiastical appointments as well as battles) as I will provide in a link below are very sparse in terms of actual descriptions of anything about the Danes but this battle happened and x won... In England at least, it should be noted most invasions by the people we think of as "Vikings" (To go Viking meant to go raiding, there was no such "culture") were Danes and Norse, with a sprinkling of Frisians etc, for the most part the conquests of England were Danish not Norse.

Anglo Saxon Chronicle: http://www.gutenberg.org/ebooks/657

They seem very safe as sources as they're written in relatively neutral tone. Then you have writing from Churchmen such as Asser and Bede which I honestly haven't personally read so can't speculate on. Bede lived in Lindisfarne, a Monestary raided by the Vikings so presumably had an axe to grind, Asser was a partisan of Alfred so would've been writing from a Wessex-centric (and especially Alfred) perspective rather than an objective one. Never is their Christianity really a factor though..

But that's just a logical interpretation based on their writers and origins. Someone familiar with the texts no doubt could do much better, I'm sadly out of my specialty in this period. I know H. Gneuss. produced a paper I cited once many moons ago called "Handlist of Anglo-Saxon Manuscripts: A List of Manuscripts and Manuscript Fragments Written or Owned in England up to 1100." in the journal Medieval and Renaissance Texts and Studies 241 (2001) which allows you to select the Christian account of your choosing and evaluate it individually...

Safe to say though that they're (if mildly hysterical at times) in general fairly reliable except where there's a direct reason for them not to be. I believe the answer must then be "You can't generalize accurately about a huge number of sources by different authors, just based on their religion"