Easy example at the moment, I think it is obvious from game theory that there are situations where a rational actor in the US would order a nuclear strike on Russia. Under such circumstances, I'd rather the person with the power to do so acted irrationally. Following this line of thought, it is reasonable to support extremely religious people with irrational ideals for high office - as long as what they actually do gets a good outcome. Eg, a strong belief in a higher power might sometimes drive the sort of people who are willing to decentralise executive authority amongst the masses.
I believe it’s part of human nature. It’s exhausting being totally rational
1) "If you really have to pick a belief system to put your faith in, you can do much worse than traditional religion." Now, I'm a lifelong atheist, and atheism is one of the few things I never changed my mind on, but I came to the conclusion that this is probably true: at the very least, traditional religion is a stable belief system that won't destroy your life.
2) "A lot of people who aren't traditionally religious, actually follow some random bullshit creed that's much worse than religion." I agree with this, there is a genuine human need religion fulfills and many might want to "fill the void" with subpar alternatives.
3) "If you are an atheist, then you necessarily fall into case (2)." Which is blatantly false, as the existence of millions of perfectly well-adjusted and functioning atheists shows.
That might be true in liberal western democracies, but there are many parts of the world where your particular choice of religion may well destroy your life or straight up get you killed, if the people behind the next coup don't share your beliefs. Even in the west you might hinder your own success if you pick a non-majority system.
Religious people in America act religious on Sunday and like ruthless, immoral "greed is good" capitalists on Monday, flexibly switching ideologies for their convenience.