There's a reason we can all agree on theism as a good source of examples of irrationality.

Let's divide the factors that lead to memetic success into two classes: those based on corresponding to evidence, and those detached from evidence. If we imagine a two-dimensional scattergram of memes rated against these two criteria, we can define a frontier of maximum success, along which any idea can only gain in one criterion by losing on the other. This doesn't imply that evidential and non-evidential success are opposed in general; just that whatever shape memespace has, it will have a convex hull that can be drawn across this border.

Religion is what you get when you push totally for non-evidential memetic success. All ties to reality are essentially cut. As a result, all the other dials can be pushed up to 11. God is not just wise, nice, and powerful - he is all knowing, omnibenificent, and omnipotent. Heaven and Hell are not just pleasant and unpleasant places you can spend a long time in - they are the very best possible and the very worst possible experiences, and for all eternity. Religion doesn't just make people better; it is the sole source of morality. And so on; because all of these things happen "offstage", there's no contradictory evidence when you turn the dials up, so of course they'll end up on the highest settings.

This freedom is theism's defining characteristic. Even the most stupid pseudoscience is to some extent about "evidence": people wouldn't believe in it if they didn't think they had evidence for it, though we now understand the cognitive biases and other effects that lead them to think so. That's why there are no homeopathic cures for amputation.

I agree with other commentators that the drug war is the other real world idea that I would attack here without fear of contradiction, but I would still say that drug prohibition is a model of sanity compared to theism. Theism really is the maddest thing you can believe without being considered mad.

Footnote: This was originally a comment on The uniquely awful example of theism, but I was encouraged to make a top-level post from it. I should point out that there are issues with my dividing line between "evidence-based" and "not evidence-based", since you could argue that mathematics is not evidence-based and nor is the belief that evidence is a good way to learn about the world; however, it should be clear that neither of these has the freedom that religion has to make up whatever will make people most likely to spread the word.