I think its more her epistemology that scares me than any one or two particular stances. It would be yet another President who thinks it better to make decisions based on their interpretation of a 2,000 year old book than through science, logic, and reason. We've seen what 8 years of rabid anti-intellectualism can do to us, and the ill effects might start compounding rapidly.
I hardly think it's fair to take someone's religious beliefs and infer their intellect. Someone's beliefs about the unknowable (or lack thereof) doesn't have a causative effect on their intellect in any way I can determine.
Imagine the power a person would have as president: being able to call up the SEC chairman or the Fed chairman for an hour gives him more power than any entepreneur I know. If Bush is a complete bumbling idiot, surely some enterprising entepreneur would have been able to outsmart him in an election. Seeing as how that didn't happen, I'm forced to conclude he's at least slightly more intelligent than he appears.
Have you ever heard Tony Blair speak for any length of time? Blair appears to share many of the same views as Bush, but tends to express them much more clearly. I don't agree with Blair on many points, but the reason I disagree is not because Blair is an idiot; it's because he is working from a worldview / set of assumptions that I don't share.
I'm voting you up and asking you expand your observation.
We've seen what blind rationalism and blind belief both can do in 300 years of having people attempt to run their own governments. Your concerns are hardly new, and there's a lot of history to draw upon.
A moderate balance of faith in something greater than ourselves, humility, and the ability to hold reason as the highest of all virtues seems to work best -- or at least it has in our country's history.
Pure faith and pure logic alone are funny things -- they tend to bend to the emotional and cultural currents of those espousing them. And usually without the person's awareness.
We've had radical swings between rationalism (such as when we were founded), to faith, back to rationalism again, and back to faith. Each generation feels like it is the first or the only one going through something. We've been here before, and we'll be here again.
Hope I'm not trolling for an argument. That is not my intention, anyway.
The thing about faith and reason is this: You can't have one without the other. All reasoning must be from some first principles and first principles are always a matter of faith.