Upvoted. To extend Eliezer's favorite metaphor, rationality makes it easy to get where you're going by making the map closely match the territory, but merely having a good map won't tell you where you want to go.

Also upvoted, and very succintly put.

Rationality is a tool we use get to our terminal value. And what do we do when that tool tells us our terminal value is irrational?

Never ask that question.

I agree, and I think that pretty much answers the post's question:

What would you do if true rationality requires giving up something even more fundamental to the human experience than faith?

"True rationality" is, pretty much by definition, the best way of achieving your goals. The above question should be written as: do you have goals that are so important, that you would agree to give up something fundamental to the human experience to achieve them?

My personal answer is: mine only such goals are of the form "do not undergo a huge amount of torture/suffering".