Classical physics is completely based on rationality, except perhaps for gravity propagating faster than the speed of light.
But quantum physics, one might say, is completely irrational. Its saving grace is that with clever manipulation of mathematics, like renormalization, it can obtain incredible agreement with experiment. But that does not belie its fundamental irrationality. It can only calculate what is invisible and undetectable. Then it does probablistic averaging over the invisible fields to obtain what is detected. There is no understanding of the individual detection process going from the invisible fields to the excitation of an electron.
And if that were not irrational enough, we have experiments that are so far from rational understanding that the results are just given a name, like entanglement, that conveys a sense of understanding. But in truth no one has any idea how particle pairs are entangled so that they know about what is happening to each other instantaneously although separated by significant distance. Again the speed of light law is broken.
When we get to the realm of string physics we encounter concepts like multi-dimensional universes that when previously proposed in mysticism were labelled as irrational. Well making them the assumptions of string and brane physics does not alter the fundamental irrationality of these assumptions. And in this case the irrational theories are not rescued by agreement with experiment. There are no experiments that apply to string physics.
The fact that quantum physics is rescued by experiment actually proves that the universe is fundamentally irrational. So arguments that its rational to be an atheist and only believe in science, in my opinion, are short-sighted because quantum physics, the basis of all low energy science, is fundamentally irrational.
And furthermore now we have mathematicians like Godel and Chaitin telling us that math is rather irrational is the sense that math is incomplete (you cannot derive everything from the axioms) and fundamentally random (there are only islands of rational math, and even they are incomplete)
So why base your beliefs on rationality when reality is fundamentally irrational. Irrationality is no longer a ligitimate basis for rejecting things you do not want to believe in. Just reject them because you want to, and admit it.