Some celebrities are very easy to imagine living in isolation, sending their staff to the store for groceries, or having no idea what groceries they even have, just expecting when they go to the closet there'll be toilet paper waiting, and that a meal will appear every evening. Most of them, really. There's no conflict with the idea that they might be hard-pressed to go out into a store without being flocked with unwanted attention because they wouldn't have to go out into public.
But a lot of other celebrities, when they're not on tour, you have to imagine they go to the supermarket, and maybe even the mall. Some of them can get away with it, I'm sure. If you saw Bruce Springsteen in the supermarket, he could probably just be casual and if anyone asked for his autograph or started to natter on at him about how much they loved (or hated) his work, he'd probably be cordial and be able to get on with what he was doing quickly enough. (At least, that's the public image he projects, but since this is a public-image thing, he'd pretty much have to behave in accordance with it.) Or if he wanted he could say "nope, not him, I get that a lot" and pull it off.
But just try to imagine Jenifer Aniston shopping for shoes at the mall. Just to make it work, don't you have to picture a cordon of security goons at 50 feet away keeping the rest of the crowd away, or her shutting down the whole shoe shop so it's just for her? And even then, it's not really credible. Surely, she has personal shoppers who work for her personal shoppers. She probably tries to be appreciative of fans, since she loves to be appreciated, to a point, and then she's just exasperated. (Again, how much of this is deliberately-projected public image? And does it matter?)
Obviously, they can send staff to do most of their shopping, and handle many of the things that the rest of us do in public. But what about the things you have to be there for in person? Do celebrities go to special doctors that only see celebrities so there's no awkward moments in waiting rooms? Do they get special treatment in hospitals to avoid their treatment being interrupted by fans? Are they able to get their driver license photos taken in private or do they have to endure those awful long lines surrounded by gawkers? Flying first class avoids some of the difficulties of air travel, but what about the security checkpoints and the waiting rooms at the gates -- or do they always just take private jets (and if so do they have their own security checkpoints, or are private jets immune to that part)? Do they go to the same polling places as the rest of us to vote?
I guess one reason a lot of them live in one of a few enclaves of the wealthy (Beverly Hills, the Hamptons, etc.) is so that the places they have to go to do these things are used to it. They'll run into only other celebrities and people who are used to celebrities; any non-celebrity who insisted on gushing at them wouldn't last long. Still, some of them don't live in those enclaves, and they all have to travel.
I've never seen a celebrity in public, but I am inclined to think if I did I would probably not even say a thing, let alone gush at them, even if it was someone who I'd really like to chat with and who I think might appreciate it (like, say, Nathan Fillion, who rumor has it is a regular guy, a geek, and a roleplayer). I'm too shy even to talk to people I know sometimes, let alone a celebrity who probably gets harassed by strangers all the time. But there's always going to be people who will be pushy. I wonder if I overestimate how much there are, and a celebrity at a fame level of Nathan Fillion (let's say Castle-era, not Firefly-era) or even Bruce Springsteen (with the "regular joe" air about him) can get by on an occasional smile and autograph in the produce aisle no problem?