If you search the net a bit you can find many claims for the "irrationality" of relativity and quantum mechanics. I've just picked two at random here, but there are thousands like this:
"Near the origin of relativity is the claim that the velocity of light is determined by the receiving point. Effect supposedly precedes cause. Everyone knows something cannot be caused after it occurs. That claim is not allowed anyplace."
"The Natural Philosophy Alliance (NPA) is devoted mainly to broad-ranging, fully open-minded criticism, at the most fundamental levels , of the often irrational and unrealistic doctrines of modern physics and cosmology; and to the ultimate replacement of these doctrines by much sounder ideas developed with full respect for evidence, logic, and objectivity."
-- (The group's site is down right now, so no link!)
Now, certain "Austrians" have, quite detrimentally to the greater acceptance of Austrian economics, linked such crank physics to the Austrian programme in economics. This rejection of mathematical or physical findings due to their "irrationality" is a phenomenon which has arisen again and again in the history of science and mathematics. In every single case given to us by history, it later became clear that the "irrationality" was entirely that of the "rationalist" critics, who were unable to extend their own thought processes to embrace the rationality of the new mathematical or physical findings.
Here are just a few cases which some advance in physics or mathematics was deemed "irrational" by numerous "rationalists" at the time it occurred:
Irrational numbers: It is said that the Pythagorean who first discovered that the square root of two is irrational drowned himself.
Negative numbers: How can there be less than zero of something?
Imaginary numbers: Hey, they're imaginary, aren't they?
Heliocentrism: Critics of Copernicus said his model was crazy -- which, from the point of view of Aristotelean physics, it was.
Action at a distance: Huyghens and Leibniz, amongst others, chided Newton for re-introducing "occult" forces into science.
What is quite striking is the each new wave of critics of the advance of science and mathematics holds as 'a priori' conditions of 'rationality' precisely those physical and mathematical findings of earlier generations that were previously held to be the height of 'irrationality'! Surveying this process, we can easily discern what is occurring: for many people, intellectual growth has ceased by, say, 20 or 25. Whatever concepts they have absorbed by that point in their lives are deemed 'rational'. Any new concepts they encounter after that point are 'irrational'.
Relativity and quantum mechanics, as shown by the great Ernst Cassirer in what is, perhaps, the best book on the philosophy of science I have read, entitled Determinancy and Indeterminancy in Physics, are as fully rational as -- and, in some ways more rational than -- ealier paradigms of physical investigation. What's irrational is to reject the findings of modern science because they strain your brain.