Ok, I can kind of see how you'd do that. Religion is present everywhere in Northern Lights, but acts mainly as a motive rather than a plot element. Magisterium as generic authoritarian state-like institution with no well-explored motives
performing nasty experiments on children. Young child must rescue friend. Don't explain theory as to what Dust is. (but doesn't that leave people wondering what the hell is going on?)
Incidentally, I am impressed they didn't age Lyra too much by casting an older actress. It's important to the story that she be around 12. Ageing her to 15, which would have been very tempting, would have resulted in the plot being a nonsense, or severe changes to it.
But they plan maybe to make sequels if this does well. Which leads to an obvious question... How on earth can you do the same thing with the next two books, which have religious elements far deeply entwined into the core plot. If the Church is complaining now, then how loud would it complain for those?