FreeBSD has good support for DEs with XFCE and Lumina, anyways. At least I've never had a problem.
I was able to get a compositor (Compiz) working on Mate and this fixed the tearing issue. It had some issues where it just kept crashing and rebooting that I never figured out. So I switched back to Gnome3. Although Gnome3 comes with a compositor (I think? And I think it might be Compiz?), I can't seem to get rid of the screen going black when a video starts.
But it really doesn't make a big difference and it's not a big enough annoyance to matter. I don't really use FreeBSD for media anyway. It's just the auto-play videos on Facebook that triggers the infrequent frustration.
I think Lumina is looking really promising, though. I recommend giving it a try if you have the time.