The PR associated with this build originally had [ci skip] in its commit message. When I pushed that commit, the build ran anyway - but only the last job in the workflow:
https://circleci.com/gh/theliturgists/app/482
This, of course, is entirely invalid; it appears to be building using caches from previous builds, even though 1) the cache key file changed; and 2) [ci skip] appeared in the commit message.