@justsomeone and me talked a bit more about the topic and we found out it is not the Firefox Developer Edition itself, but another config option that I apparently switched off some time ago.
about:config 
security.fileuri.strict_origin_policy targets specifically local files (file:///) and when set to false will allow the loading of the subtitles. It defaults to true.
Where I was right was
This problem was fixed in bug Bugzilla 1558299 and the config switch security.fileuri.strict_origin_policy was introduced to help developers with exactly the problem discussed in this topic.
Michael