Are there specific videos it happens on? For example, are they YouTube movies?
I could see them actually enabling HDCP on those types of videos. It’s a type of DRM encryption and is used by Netflix and Amazon Prime, and likely other streaming TV. I believe I’ve read that YouTube uses it for similar content.
The reason I bring it up is that I would get this weird scrambling effect on my old monitor, as it didn’t support HDCP. It would show the screen every once in a while, but then it would jump to colored static.
Alternatively, YouTube could be experimenting with some codec changes that aren’t compatible with all systems. One way to check would be to try the add-on Enchanted h64ify on your desktop browser, and see if disabling any particular codecs makes the problem go away.
That said, it would be weird for an updated Apple device not to handle the latest codecs. Another idea is that something is going wrong at your local YouTube cache. Are the reports of problems generally by people in the same geographical region?
Those are all I can think of off the top of my head, and only one you can do even remotely anything about. Sorry.