[Note: This similar Q concerns the same bash error message. It's been marked a duplicate of this other Q. But because I found a very different source for this error, I will answer my own Q below.]
This previously working bash script line
while ... do ... done <<< "$foo" one day started producing this error message:
cannot create temp file for here-document: Permission denied
ima_policy=appraise_tcbkernel parameter) with combination of/tmpnot beingtmpfs. But this is not really a common case :).