Why religious belief isn't a delusion – in psychological terms, at least

Religious beliefs are typically incompatible with scientific evidence and observable reality, but aren't considered to be delusions. Why not?

If someone told you, in all seriousness, that they talk to invisible beings who control the universe, you'd probably back away slowly, nodding and smiling, while desperately looking for the nearest exit or escape route. If this person then said they wanted to be in charge of your life, you'd probably do the same, but more urgently, and with a view to finding the nearest police officer.

And yet, this happens all the time. Arch Brexiter, unlikely Tory leadership candidate and human Pez-dispenser Jacob Rees-Mogg recently blamed his extreme and unpleasant views on his Catholicisim, which was seen as a valid excuse by many. Current placeholder prime minister Theresa May has made a big deal about how her Christian upbringing makes her suitable for the role. And despite the lawful separation of church and state, every official and wannabe US president has had to emphasise their religious inclinations. Even Trump, whose enthusiasm for maintaining the noble traditions of the presidency can be described as limited at best.