This is always going to be a difficult question to answer (and it might get closed, I'm not sure whether it is within scope) but here goes... the answer is several fold..
Other books stole the thunder
I think there were other popular books at the time that were more obviously problematic to strict Christian households. Whilst Pullman is extremely critical of religion in general it is in some ways not very obvious.
Criticism is somewhat subtle
The criticism is not levelled specifically at a recognisable religion - for example there is no mention of Christianity in the book, and although areas of the Church do resemble Catholicism it is not laid on thickly.
I think this makes the criticism more palatable.
Indeed it was actually given praise by some of the more liberal elements of Christianity as being a good reminder against the danger of zealotry. (I think it is quite possible to read the books not as a criticism of religious faith, but a careful observation that not everything you believe in might be truth).
Faith actually plays a role in the books
In places the book actually places a lot of store in faith - the characters have little clue what Dust is, and although they scientifically (if haphazardly) try to find out, they tend to put a lot of faith in it being both benign and important (particularly Lyra and her reading of the alethiometer).
And in the end, after the Church is exposed for what it is (i.e. a lie) the question of a creator is left ambiguous.
More problematic, I feel, in the book is not the criticism of religion but the new portrayal of the Adam/Eve story. On the face of it this directly contradicts a lot of the teachings of modern religions, and is distinctly less subtle!
Then again the story is more complex than that; although it is about Adam/Eve & temptation on the face, Lyra and Will become utterly devoted to each other, which is probably a maxim that Christian households would approve of.
At its core the lesson from the book is that as you grow out of childhood the world becomes suddenly more real; more wonderful and more tragic. You are forced to make choices about your life that affect not only you, but the world around you (Lyra & Will's parting is tragic, and one of my most favourite endings to a book, incidentally).
I suspect this last part rescues the books in many respects - modern Christian homes are generally not so strict nowadays and so for most it appears to be a decent fantasy book with some key life lessons.
For the more strict doctrines, sure there are problems, and criticisms. But they were never very vocal (at least to my recollection).