Some sort of religion, even if it's non-religion, is almost necessarily going to be in your culture because religion has been and remains the major source of governmental authority in culture. Even in the US, the concept of separation of Church and State is itself, a religious idea, just as is democracy, due process, elections etc.
This is not to say that Freedom, Atheism, Reason, Science etc ARE religions, just that they can be seen as such and, from the standpoint of most organized religions, often are seen this way though few I know of insist on it as a point of their doctrines.
The American version, in fact, is much closer to the Ancient's beliefs concerning religion than the Medieval. The Romans, frex, were, contrary to popular misconception, actually very tolerant of a great diversity of religions throughout most of their history, as long as you sacrificed to the Emperor as well. The fact that the Christians wouldn't do this is the reason they were martyred, not because they denied the reality of Jupiter and Venus. Sort of like the people who want to arrest those citizens who burn the flag, yes? (not that I do, either burn it or want to arrest anyone, but it's the same sentiment)
According to someone very few citizens of Athens or Sparta would say they loved the gods, but most all of them respected them
The thing I think you must remember is that religion is really a matter of GOVERNMENT, and if you are going to make it any significant part of your plot then you are going to veer into politics at one point or another, it simply cannot be helped.
Btw, Pullman has said that HDM was a rewrite of Paradise Lost with God's Kingdom re-envisioned as a Republic.