I always liked the saying "philosophy is about what questions you ask, science is about getting answers to those questions."
On topic (or OP topic at least) I think the conflict comes from one thing.
If everything between the |s is the sum of all knowledge, and everything between the ()s is the sum of what we know right now:
Science:
|(-----------KNOWN---------)----------UNKNOWN-------|
Religion:
|(-----------KNOWN---------)-----UNKNOWN-------/-----GOD-------|
That's slightly simplified, but religion is attemtping to confidently give answers about things which fall into the unknown section of knowledge. Science doesn't claim to prove that God does or doesn't exist (though it can fairly easily disprove the truth of most of the literal readings of a lot of holy books), but religion claims answers where it cannot possibly have them. Which is fine in the privacy of your own head, but when it attempts to enforce those beliefs upon people who do not agree with them is just downright rude
There would be no conflict if the religious section of society actually respected the rights of everyone else to not believe the same thing they do and just get on with their lives within societally accepted boundaries of morality and ethics however they liked, but instead they try to claim that because their religion is for or against something that everyone should automatically be forced to live by those same rules and beliefs. Science didn't start the fight, unless you count finding out true things about the world that directly contradict the magic books...