So I removed all proprietary codecs from my Fedora installation and installed the new free MP3 implementation from Fedora's repository. This allows me to play MP3s in Rhythmbox and in Chromium.
However, playing any HTML5 audio with MP3s in Firefox 54 will fail. HTML5test.com reports no support for MP3 on Firefox but everything seems fine in Chromium.
Before I installed the free codec, neither worked, so the two applications don't ship with their own codec (which was expected). Now I am wondering what is missing for Firefox to be able to play MP3 audio?