It seems Firaxis' engineers could use a few language lessons, because it just so turns out that a simple spelling error in one of Civilization VI's data files was behind the AI's strange behaviour, and Firaxis agrees.
Tucked away inside Civilization VI's Leaders.xml file were several rows, which dictate AI leaders' priorities throughout the game. In this isolated block of five instances - the word 'yield' has been spelled as 'yeild', which turns out to have driven the AI mad for faith.
The full code line went like this - "Row Item="YEILD_PRODUCTION" ListType="DefaultYieldBias" Value="25"", with four more instances for Science, Culture, Gold and Faith. So even though both human and AI Civ leaders prioritise production and gold over faith, the error turned some AI into religious fanatics.
With the error easily reproduced, many went and fixed them themselves. Further testing indicated success as well, with AI players finally acting like they should.
To be fair, the guys from Firaxis turned out to be sports about the entire thing, responding in a light, humorous tone. Of course, we'll disregard all the tables flipped over the darn AI.
Responding to an enquiry by PCGamer, Firaxis stated "We’re aware of a community-reported bug that has a minor impact on AI behavior. We’ve also made sure that everyone knows that I goes before E except after C… or other weird exceptions. Thanks to all who helped bring this to our attention and there will be a fix included in our next update."
Well, there you have it folks - a herd of elephants can indeed sometimes be chased away by a mouse, as small as a spelling mistake. Thankfully though, we can all now get to playing some Civilization VI.