After being abruptly awakened on Saturday morning at 4am (nightly cron job for yum updates), we found that an upstream RHEL/CentOS update had changed the minimum acceptable length of DH keys to 768 bits.
This is a companion discussion topic for the original entry at https://www.funkypenguin.co.nz/note/openssl-101e-30-broke-sendmail-mysql-on-rhelcentos-56/