Never meet your hero. There are some well known people out there that are great human beings, but just as many who are average or below, and being a celebrity won't help a bad personality get better (usually).
Not only for the reason to keep the illusion, but if I saw someone famous in public I wouldn't be that annoying fan that helps push some to the edge. At best I'd just mention I liked their work (not even saying specifics) and let it be. Again, they are people, and I know I don't like to be bothered with small talk from strangers.
A side note that is a bit related to breaking the false image. When you figure out that your parents and other relatives are just people too, with their own greatness and flaws. It's probably healthy in the long run, but the first shock can be nasty.
I guess I should name someone. Tom Cruise is always the first in my mind. Some incredible work, but he's both weird and given how embedded he is with Scientology, can't be that great of a person to know well. But maybe not... he is peculiar though.
I would love to meet the cast of Andor and Tony Gilroy, they seem amazing, intelligent, and down to earth. But going back to my point, at most all I'd be doing is telling them how great they were at their job, and hope that what they portray in interviews is who they really are.