Order...
ToD happens before Raiders. I noted someone mentioned it as a sequel, which in the theaters it is, but chronologically it preceeds RotLA.
As for Indy's beliefs, he strikes me as agnostic for starters...a scientist in search of "fact, not truth." I know, that's from TLC, but that's where we meet Indy in ToD...he's quite objective.
By the end of RotLA, he seems hooked on the awe that comes from the supernatural, and by TLC's close, even though we don't get any real insight into what he believes, he seems less skeptical of things relating to the supernatural in general and Christianity specifically.
"Oh, I believe, sister. That's why I'm down here." The way he says that in KotCS makes it sound like he means "I believe these creatures are real; that's why I'm over here and not up there next to you...so if they're going to melt our faces, I want a head start." The way it reads in the script, it seems like he means, "I have faith/beliefs; that's why I do what I do." I believe the latter is more accurately what that line means, despite what it sounds like in the film.
As a scientist, Indiana would likely choose his faith based on the most solid reason. I haven't read the rest of this thread, so I don't know where you all are on that idea or if it's even been posed before now.