Is it possible for celebrities to remain anonymous in public without being recognized, even by accident?

Michael Caine tells this story about a fairly well-known movie icon:

Sure. …

I had a very funny moment with Cary [Grant]. We were talking outside a hotel in Los Angeles when a woman came out. She suddenly saw me and said, “Michael Caine! I have been in Hollywood for two weeks, I’m just leaving, and you’re the first film star I’ve seen. You’re the only one!”

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Then she turned to Cary Grant and said, “You never see films stars in Hollywood, do you?” And Cary said: “No. You. Don’t.”

Then there is the (maybe apocryphal) story of the frugal Grant standing in line at a MacDonald’s, where he is noticed by a customer. She says, “You know, you look like Cary Grant.” And Cary Grant looks at her and says, “Would Cary Grant be standing in line at MacDonald’s?”

At which point my friend, like a lot of thirteen-years-olds, got more ambitious and asked if he could visit Disney’s Burbank studio. Disney nodded and looked at the man he was with. “Ken here will give you his phone number. Just call him and he’ll set something up.”

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In 1961 a friend of mine, then thirteen years old, noticed Walt Disney walking down Disneyland’s Main Street with another man. Nobody paid Walt the slightest attention. He wasn’t in a suit, his grayish hair was without quickie dye for a movie camera, he wore no makeup. My friend fell in step beside Disney and asked for an autograph. Disney nodded, scribbled his name on the back of my buddy’s ticket book, and maintained his pace, saying if he stopped he would be “a dead duck”.

Whereupon she shrugs, nods, and goes back to minding her own business.

Henry Cavill, longtime Superman in a long line of Supermen, stood under a New York City billboard displaying “Henry Cavill as SUPERMAN!” He wore glasses. Nobody recognized him.

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Ken stopped and gave my friend a business card. Walt halted as well. A woman standing fifty feet away yelled “Walt Disney!” and pointed. Like that, a couple hundred people headed in Disney’s direction. As they started to surround him, Walt vanished through an employee entrance. He was right about the “dead duck” thing. (Note: this is a replay of an earlier post, but it fits the question.)

Addendum: My father, who’d worked as an artist for Disney since 1938, took my kid brother and me to Disneyland the summer of 1959. While we kids were off doing rides, my father spotted Disney talking to somebody in front of the Enchanted Tiki Room. Walt was wearing a Hawaiian shirt, straw hat, sun glasses. Nobody gave him a glance. My father walked up and scratched Disney on the back. Walt turned around, said “Oh hi, Ralph,” and they chatted for a few minutes before going their separate ways. Another example of Disney being unnoticed when out of his usual context.