The most common and most likely answer to this crossword clue is the 3 plus 2 plus 5 plus 5 letter word MEN IN WHITE COATS
I've seen this crossword clue in The Guardian
M
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More clues leading to the result MEN IN WHITE COATS
Buddy explains!
The straight part
We know that "Are they sent for if popes, say, act so strangely?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case are they sent for if popes, say, act so strangely? = men in white coats.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.