Your presentation of our religions as attempting to be directly congruent with the Viking-era Norse is fundamentally inaccurate. Our religious traditions extend outside of the Viking-age, and outside of just the Norse, not to mention were infinitely varied within Norse culture to the point that the only conclusion we can draw is that here was no dogma or unifying traits outside of a shared cultural heritage that goes back to Proto-IndoEuropeans as indicated by the evolution of languages and the importance placed on gods with the same or similar names throughout the larger Germanic, and PIE relatives. It also comes forward into the Christian-era with many religious traditions becoming part of folklore.

The entire accusation that we are ignoring our Christian ancestors is just plain laughable, as is the idea that we don't know if sources were doctored by Christians. For many of them it is highly probable, for others there are clear references and linguistic choices that help date poems as being older than when the surviving texts were written. This would indicate either an extremely strong oral tradition or older texts that have since been lost, both of which maintained linguistically accurate (and therefore presumably factually authentic) phrases and attestations.

Not that it even matters, because we can also tell from the changes (place to place, time to time, culture to culture) these were highly mutable religious traditions. Someone like Snorri Sturluson writing his own version of the stories presumably would have been seen as entirely legitimate in his chronicling, considering we know people made up stories about the Gods and that this was a culturally accepted practice.

So you are correct that we do not likely say the same prayer and sacrifice the same livestock they would have 1100 years, but it is also intellectually dishonest to act as if that was ever our intent.