The following used to work:
echo TextOfMessage | mutt -s SubjectOfMessage -a FileToAttach firstname.lastname@example.org
On August 28th (according to my cronjob logs) this suddenly stopped working. It turns out (after a bit of googling) that now we have to insert a double hyphen before the recipient email address, i.e.
echo TextOfMessage | mutt -s SubjectOfMessage -a FileToAttach -- email@example.com
So it seems that on August 28th DH replaced an old version of mutt (which didn't require the double hyphen) with a newer version (which does).
Hopefully this post might reduce by some minuscule amount the quantity of hassle in the world.