A few apps have been showing pop-ups warning users in advance that they are not going to do the verification. Obtanium is definitely on of them. I think I saw something similar on NewPipe.
It says they will not comply with whatever registration is required. It does not say specifically what they will do, in part I assume because they had not been given enough specifics (for example if it remains possible to sideload but not to be in a third party app store, would they continue to develop with that diminished accessibility?). Additionally YouTube itself has been making some system changes that, outside NewPipe's control, may make it functionally impossible to use the service without being logged into a Google account, so they may be suggesting that they think the writing is on the wall for them.