"What I mean is that religious people claim that the existence of their God and their sacred writings are unchanging and beyond challenge, and that this view is very different from the scientific approach."
Actually that is true of islam who claim that the koran is the word of god and not subject to revision, alteration and and especially not subject to any interpretation by infidels...
However as far as I understand that is not true for most christians where the holy book and sacred writings are a collection of "Gospel according to ..." booklets and thus cannot be interpreted as being the word of God, at least for the most part...
Religion does seem to be some bedrock factored and hardwired into the fundamentals of our collective being and probably essential to the formation and prospering of our families and communities as a set of shared beliefs and common ideals that bind the community together in some way...
It might be an interesting and educational experience for you to do some historical research into the list of communities throughout history that have prospered and gwron with a strong declaration and belief system of no religion, no superior-being and no idols, holy scriptures and holy ceremonies...
I suspect that the list would be quite short, probably in the zero range...
Of course that does not mean that religion is some mystical factor that transcends humanity and the scope of our lives but merely that it can be and is represented as such...
and as we have seen through history, does not mean that it cannot be hijacked, distorted and abused for the profit and power of a group of people...
