Depends. If you are a really recognisable persona and you just log out one day, then expect a bunch of psycho-fan creeps looking for you in the real world.
An identity that is obviously constructed (like VTubers) at least signals to the audience that the real person behind the character would like to stay anonymous. I think the majority of fans would respect that wish.
Whereas celebrities who make their real-life identity into a brand - even if that brand is an obvious fiction as well - signal the opposite to their audience.