I'm not sure how much of a "movement" is taking place, but I am dead sure it should not be described as "anti-rational."
With all of the structures and technology humans have been able to build, not a single one throughout history, let alone all of them combined, have been able to design and construct a living, human being, let alone a living organism. Imagine them trying to do so using neither design nor intelligence.
If anything is "anti-rational," it is the notion that a living organism could come about without the presence of either intelligence or design. That is "anti-rational" to the point of absurdity.
I am surprised at the number of people who think a serious diaglogue is warranted to defend the mere probability of intelligent design, but I will take it as further confirmation of the biblical teaching that man would rather be purely "anti-rational" than face the prospect of accountability to someone other than himself.
Well, no, since then you've got to ponder who designed the designer and so on, ad nauseum. That's about as "anti-rational" as one can get.