The reliious based themes are presented throuh the Magisterium, Pullmans representation of Christianity and Authority.
Pullman says in an interview with Rowan Williams:
"The figure of The Authority is rather easier. In the sort of creation myth that underlies His Dark Materials, which is never fully explicit but which I was discovering as I was writing it, the notion is that there never was a Creator, instead there was matter, and this matter gradually became conscious of itself and developed Dust. Dust sort of precedes from matter as a way of understanding itself. The Authority was the first figure that condensed, as it were, in this way and from then on he was the oldest, the most powerful, the most authoritative. And all the other angels at first believed he was the Creator and then some angels decided that he wasn't, and so we had the temptation and the Fall etc - all that sort of stuff came from that. And the figure of Authority who dies in the story is well, one of the metaphors I use. In the passage I wrote about his description, he was as light as paper - in other words he has a reality which is only symbolic. It's not real, and the last expression on his face is that of profound and exhausted relief. That was important for me."
In our reality, the soul is invisible. We can only see a person's body, not his or her soul/spirit. We cannot exist in this world without the immaterial aspect. It is critical to our present existence. It drives our being. In The Golden Compass, the souls are embodied but remain close to the person they belong to. Interestingly, when the soul is harmed the person hurts, and vice versa. This is a good illustration of the biblical truth that some things damage us inwardly by damaging our souls, though it may not be clear from the outside. These can be emotional wounds, pscyhological scars, sinful thoughts and desires, etc.
Lyra's use of the athiometer to see the truth is a symbol of reality; the truth is present but not everyone can see it. She uses this instrument to find out the truth. In the Christian world, truth is fully embodied in Jesus Christ. He declared, "I am the way and the truth and the life" (Jn. 14:6). Those who look for truth and find Christ find truth. And apart from an alethiometer, they can offer prayers to God seeking wisdom and truth.