If you're asking for a YouTube website equivalent, that would be SaaSS even
if the FSF would somehow support it. Not a good idea in general. They're
hosting https://media.libreplanet.org/ but that is for THEIR needs, and only
they can upload things, so that doesn't make it SaaSS.
If you're asking for a software equivalent, well MediaGoblin is probably your
best bet. It is completely freedom-compatible and also takes care of using
proper codecs.
If you're asking for a way to view YouTube videos without proprietary
software, what I'm currently using is the mpv player with youtube-dl in it.
For example like this:
$ mpv --ytdl-format bestvideo+bestaudio
https://www.youtube.com/watch?v=m099dYl0Rhs
This way you can even watch 1080p 60fps video if you so wish. You can always
choose the format yourself. Capital L toggles looping in mpv, so you can also
loop videos infinitely if you want. It's also possible to only download the
audio if you're listening to music videos by choosing only the DASH audio
format. Saves on bandwidth and processing power. In the end though using
YouTube for streaming things means using SaaSS. But you can of course also
use youtube-dl itself to just download videos that are interesting to you, at
that point YouTube becomes more of a download server and you can playback
everything locally using your own computer, which is probably the best
method.
I would also invite you to make a MediaGoblin instance for you and your
friends to use, but that involves certain costs depending on the scale. A
working 3rd party instance from "someone" that seems to work quite well and
that everyone can upload to is https://goblinrefuge.com but as soon as you're
using other people's computers to host videos there's not much difference
compared to uploading them to YouTube.
