That would be the prophecies of St Malachi. According to Apocalypse Wow!, the prophecies are almost certainly a fraud written a few centuries after Malachi’s death. They are very accurate up til that date, then miss like crazy.
Considering that there were a Anti Popes and Hidden Popes, the list may have run out several Holy Fathers ago.
Forgot To Address The OP
No True Scotsman, Strawman and bad reasoning.
I have found that many atheists can’t accept that some people truly do believe. Yes, some theists are just going through the motions. Others feel a divine presence in their daily lives.
I haven’t read the book, but it seems you may have missed an important point: its author appears to concede that merely “feeling a diving presence in one’s daily life” is common enough, and valid in the sense that it’s a real feeling, but that the word “religious” is taken by most people to mean something rather more than this – specific tenets that, if carefully examined, would cause behavior contrary to what people really do – and that it is in this realm that many people say they are religious but, in some sense, really “aren’t.”
To avoid confusion, I think it’s perhaps best to use a word like “spiritual” for the feeling you describe. True, there is a fine line between a mere vague feeling of supernatural presence (akin to optical illusions, false pattern recognitions, saccades, and other quirks of the human brain), and a more specific, “developed”, personal “god”, and that the more someone subscribes to the latter, the closer they come to being “religious” as the author defines it. However, fine as this line is, there is a difference between the two; and people who are closer to the “mere vague feeling of supernatural presence” end of this continuum, while perhaps mistaken, do not embody the contradiction which is the author’s main theme.
Even strident atheists, I’m sure, would “go easy” on this latter group of people*, since the human brain is, by its nature, full of tricks and limitations. (Strident atheists who have, say, taken LSD, might be especially inclined to “go easy” on them.)
(*the “mere vague feeling of supernatural presence” folks.)
Religion itself is a merely one of those “provisional explanations for immediate situations.” Yet even long after this “provisional explanation” has largely ceased to be useful or constructive, most of us still “don’t spend much time trying to reconcile (religion) with a unified large-scale logically consistent model of the universe.”