I prepared 3 video formats for my site:
/assets/video/background-purple.ogg
/assets/video/background-purple.webm
/assets/video/background-purple.mp4
I believe this problem is related to a bug stemming all the way up to FF 20, where a lot of the popular webm encoders are inserting negative timestamps and firefox can't play the video until it downloads the whole webm file: https://bugzilla.mozilla.org/show_bug.cgi?id=868797
The fix is mentioned in the comments:
ffmpeg -i input.webm -codec copy -avoid_negative_ts 1 output.webm
The important encoding flag being -avoid_negative_ts 1