Religion and science. Both address the big questions of life. And they do that from two mutually exclusive viewpoints. At least, that’s what most people agree on. But not all.
Many years ago I saw a book for sale: The psychology of religious knowing. It didn’t look peer-reviewed, but it evidently was meant as a serious scientific book. I was fascinated! Religious knowing? I was not sure if the authors had been studying people that claim to have religious knowledge, or that they claimed to have that knowledge themselves, and studied it. In the first case it may have been interesting science. A lot happens in the name of science, and it is very relevant to have psychological insight in those who act thus. And you may never find out if those who claim to read God’s mind really believe themselves that they do, or that they enjoy using religion as a justification to serve their own goals, but that is just one of these complicating factors of social science. (It would not surprise me that if you toss someone’s head in a CAT-scanner you may be able to see the difference through observing which part of the brain fires when, but I have problems imagining the big players in world religion volunteering to undergo such an experiment...) Social science is not, and never will be, natural science, but that does not mean it is not valuable, and social scientists have, as far as I know, come up with an impressive array of tricks to deal with that complication.