Logically the next step is to scan for any copyrighted content and notify authorities that you're watching a movie without paying for it. After all, it's all about catching criminals, how could you possibly object.
Just to be clear, "false positive" in this case means an innocent person is accused of trafficking in child sexual abuse material. It's likely they will be raided.
Sure, that's bad if you're Apple, but it's a lot worse if you're the alleged predator.
Which could also be spun as "Apple allows X freebies of known/highly suspected CSAM on your device before they'll tell anybody".
The amount of PR failure that has gone into all this is huge and multi-level.
From now on, when asked to check whether a user's encrypted phone contains arbitrary content the FBI wants to know about, Apple can no longer say "we don't have a way to do that." Sooner or later, you can bet they will start doing it, whether they want to or not.
If this feature leads to anyone losing their job due to incorrect criminal accusations it will not even make the papers because we expect the accused are guilty anyway. Apple won't shed a tear until there is a class action.