I believe that religion is a big factor in literature. Most of what I wirte can be in some part linked back to the bible. I also have a story called Soliluquoy of an Angel that was very biblical.
Anything that motivates people is going to influence writing. Politics, love, success, honor, religion--most stories have elements of these. An author is naturally going to make certain assumptions about the world that become part of his or her story, and religion is a powerful worldview to have.
It depends on what you mean by religion, but in some way organized religion has affected all of us, whether to gravitate towards it or away from it. I am a Christian, but have some issues with organized religion. This doesn't necessarily means that it effects all writing, though. If you mean religion, in the sense, what one believes (aka his or her own religion) then it is a constant influence in his or her writing. For me personally, my beliefs influence my writing heavily. If I'm not conveying some sort of message, typically derived my personal belief system, then why am I writing?
Funnily enough, in fifth grade my Christian writing teacher used to tell the class never to write about God because it was disrespectful, risky, etc. So I avoided using the word "God" in my writing like the plague.
I'd say this varies with culture. In some cultures, the fact that the sun rises every day is undeniable proof of a god or gods existing and interacting with humans. Different cultures have different definitions of what constitutes "reality." This is why I have a problem reading and understanding magical realism, which might be called a kind of fantasy, because being from the culture I'm from, where real is real and fantasy is fantasy, it's hard to differentiate between "magic" and "real" when in the universe the writer created, there's no clear line between the two. This is how some cultures still see things. The old myths that were told and written down weren't intended to be fantasy, though that's often how they're treated nowadays.
That is a good point. But I mean "provable" as in scientifically provable. We can prove that the sun rises with science. But we can't (so far) prove that there is a god with science, or that it is God making the sun rises, regardless of what people believe, which is entirely different. I suppose the problem is that no-one really sees true reality. We all have our own individual versions of what we think reality is. I don't want to get into a religious debate. But it depends on your definition of "provable". I see your conundrum through. Do you mean that, whatever is really true, some people truly believe Gods are real, and believe they have proof? So to them, that is reality. So the point you're making is: how can you be sure the Gods in the writers world are real, and not just "real" in the sense that the characters believe them to be real? What is the difference?
Well, when I create fantasy settings I always start with the 'how the world was made'. I base these events in Christian religion, since I'm Catholic. Back to the question, no, I don't think a book will change my mind about it.
Also, yeah I sometimes make up religions based on ancient mythologies because... I lov 'em! And like Kratos said, my morals sometimes find their way into what I write.
Religion and fiction have a lot in common. Both require a fundamental "faith" in the story...faith being an irrational belief. To enjoy writing (or even reading) fiction, one must suspend reality and become immersed in the "story" on the basis of faith alone. Without "faith", neither religion or fiction would have followers.
Although I grew up Southern Baptist and remain a devout Christian to this day, I've never openly promoted my values in my work unless you count one of my main characters saying a prayer during the opening chapters... I try as hard as I can to keep my work clean, (no language, no sex, I really have no problem with violence, though), but I haven't necessarily been spreading the Good Will through my writing, either.