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In the Franchise/Tintin comics, bumbling detectives Thomson and Thompson would often attempt to go undercover by wearing ridiculously stereotypical disguises of whatever country they were in. One early book has them dress up in garish Chinese garb on a visit to Shanghai. They end up with a large crowd of pointing and laughing people following them. Another had them wearing traditional ceremonial garbs while undercover in Syldavia. As it turns out, they're wearing Greek costumes anyway.
In The Hebrew Hammer, the main character and his love interest try to arrest the Big Bad at a Kmart by posing as a Gentile couple, complete with Southern accents, Christian paraphernalia, and American flags.
Admiral Aladeen in The Dictator dresses head to toe in the American flag posing as an American tourist during a helicopter tour scene, where he and his cohort are Mistaken for Terrorist.
Sasha Baron Cohen is frequently accused of abusing this trope in his films.
Marty's flamboyant cowboy attire in Back to the Future III, which he did lampshade, but (1950s) Doc insisted it was fine to wear. Marty switched to more reasonable clothes as soon as he could.
Gene Wilder's pathetic attempt to pass for African-American in the movie Silver Streak.
Team America: World Police has a funny subversion. The main character's job is to infiltrate into a Muslim terrorist group. He simply wraps a towel around his head, superglues hair to his face, and says, "Dirka dirka Muhammed Jihad." It works.
In Revenge of the Pink Panther, Inspector Clouseau goes undercover in Hong Kong in Yellowface, eye makeup for slanted eyes, a Fu Manchu mustache, a rice paddy hat, and a Qipao, while all the ordinary citizens around him wear business suits.
In High Anxiety, Richard is wanted for murder and he and Victoria need to bypass airport security, so they disguise themselves as a loud, bickering elderly Jewish couple. Their reasoning is that the louder and more obnoxious they are, the more they'll be ignored.
In The Man Who Was Thursday, Lucian Gregory repeatedly tries to infiltrate non-anarchist society by disguising himself as capitalists, priests, or military men. It fails each time because he's an over-the-top anarachist stereotype of these groups.
Sergeant Colon does this in a downright racist manner in Jingo, to the point that onlookers assume he's a spy for a country other than the one he seems to be from, since no actual spy would be so obvious.
71-Hour Ahmed in the same book does this brilliantly. He keeps doing stereotypically "Klatchian" things (like offering to buy someone's wife for twenty camels) and speaking Morporkian badly, with a thick accent. It turns out that not only is he the police chief of Al-Khali, he was educated in the Assassins' Guild school and speaks Morporkian perfectly when he wants to.
The Goodies attempt to pass themselves off as Scottish is so over-the-top that the Scot they are trying to fool declares that they must be English tourists.
In Funky Squad, one of the square cops attempts to pass himself off a hippy by dressing as a cop's stereotype of a hippy. Not helped by the fact that he arrives driving a police car where he has crudely painted over the word 'Police' on the door so it reads 'Peace'.
Metal Gear Rising: Revengeance: Raiden's idea of an "Authentic Civilian Disguise" while in Mexico is a Mariachi outfit which consists of a gaudy hat and an even gaudier poncho, draped over Raiden's otherwise completely unaltered cyborg body.