Possible spoilers ahead!
As I've said elsewhere, I really enjoyed the first book, and that coming from a (very firm, some would say fanatical) Christian perspective. It is clear in the first book "The Church" in Lyra's world is evil, but that didn't bother me at all: Organizations calling themselves "The Church" in our world have often been evil. I didn't take that as an attack on Christianity of even religion in general, just that this particular group is bad and also happens to use the cross as its symbol.
It does strike me as odd that the Church in Pullman's fantasy uses the cross as its symbol, yet there is no reference anywhere to Christ. He attempts to criticize Christianity but omits its central figure.
Of course, as the stories progress, the term "religious overtones" becomes silly. The Amber Spyglass doesn't have overtones. It is about religion. Unlike, say, LOTR, the primary purpose of Dark Materials is not to create a compelling universe, but rather to criticize specific elements in ours. The fantasy is a vehicle to that end more than an end in itself.
I think that to a large degree explains why the quality of the stories declines so drastically over the course of the trilogy. In Compass the religious aspects are mere overtones and the focus is on story, characters and world-building, and it's really cool. As we work up to Spyglass, the focus shifts completely until the integrity of the story is all but sacrificed to make room for Pullman's religious message. For the sake of that message Pullman makes the narrative gaffe (among many, many others) of setting up God as the villain and then revealing that God doesn't actually exist. It's like if Frodo and Sam has gotten all the way to Mount Doom only to be told that, sorry, there actually isn't any Sauron; he's just a myth the head orc made up to intimidate people, and that Ring you've been lugging around doesn't actually do anything.
I'm frankly surprised that New Line picked up Dark Materials, considering the sloppy mess that the end of the story degenerates into. I'm betting they'll loose money on it, all told. (They won't be getting any of mine for it, at least.)