Science requires a belief which there is no way to prove, which is that what you sense is reliable.
In your view, does a belief have to be provable to be rational?
In a less philosophical vein, faith in scientific approaches requires a belief that the universe is predictable ("If we do X a bunch of times, and get result Y, it's reasonable to expect that we'll see result Y the next time we do X.").
That's actually a large (and unprovable) assumption, as many philosophers will happily tell you. Of course, by definition, an assumption is unprovable. Call it a postulate or an axiom, if you prefer, but it's still the same thing - something you take for granted, and acknowledge you cannot prove.
In the end, scientific methods are anything
but logically rigorous. The whole system of science is predicated on a method of argument that is considered fallacious in formal logical arguments.
Are scientific approaches useful? Definitely. Forming hypotheses based on what you see, then testing them is an extremely pragmatic tool for getting through life, and also for developing technology and building mental models of how things seem to work.
Don't mistake it for a logical tool, though. I guess it's fine to call it rational, if your definition of rational doesn't require logical rigor. Mostly, though, I think the word "reasonable" is used to describe something that seems intuitively correct based on observation, not "rational". Maybe it's just my social circle that uses it that way, though.
All human beings have a strong tendency to explain new observations in a way that it fits into their current worldview. We call it confirmation bias, and in some contexts, it can be a problem.
While confirmation bias is not logically rigorous in the least, it can actually be a pragmatic tool for going through life. I've never met anyone whose life philosophy was completely bulletproof - if you rethought things from first principles every time you learned information that conflicted with how you currently thought the world worked, you would starve to death pretty quickly. Thus do creationists keep their beliefs despite geological dating, and thus do atheists keep their beliefs despite soft tissue in dinosaur bones. For any worldview, there are observations about the universe that have troubling implications, I think. It's my personal belief that the human mind is just too small and simple a thing to fully know and understand the universe, and that no human will ever be able to do it, so I don't worry about having a perfect philosophy. I try to figure out what seems to make the most sense based on what I've experienced to date, and go with that, even if it's not perfect.
As far as Christians not investigating evolution - most people, regardless of their beliefs, refuse to examine other people's beliefs. It's a very common human trait - while I know very few creationists who've read Dawkins, I also know very few atheists who've actually read the Bible, and even fewer who've actually read any serious defenders of Christianity (C.S. Lewis is a decent place to start). It's pretty obvious to me that people are fundamentally selfish, greedy, angry jerks, who don't want to actually understand anyone else's perspective (I see this tendency in myself on a daily basis, which is why I believe it).
As a theist who doesn't quite buy macroevolution, I've read chunks of Dawkins, and I don't find his arguments at all persuasive. Terry Eagleton wrote a
scathing review of
The God Delusion that summarizes the apparent gulf between Dawkins' arguments and what many theists believe pretty well. However, in case I've missed something, I'm planning to do a good careful read of some of Dawkins' books again this summer, to be certain I really do get what he's trying to say. I've had
The God Delusion,
The Blind Watchmaker, and
The Ancestor's Tale recommended to me. Any other additions to that list?
Heck, even any other authors the atheists in the crowd would like to recommend?
All that to say, I guess:
When you boil it all down, human knowledge is pretty finite, and all logic, reason, and rationality depend on unprovable hypotheses. To claim you've got the whole universe comprehended, or even that you have an airtight argument for the correctness of your own worldview is, to my mind, inexcusably wrong-headed.
I know what I believe, and I firmly believe I
cannot prove that it is correct. I can argue for it, and explain to others why I believe it, but to prove it (or, in fact, anything) beyond all doubt is utterly impossible.