Weirdness Coupon

Jamie: Did you get any looks driving a truck full of pig corpses around?

Adam: A few people did slow down and stare; then they looked in the cabin, and went "Oh. It's just MythBusters."

—MythBusters, obviously

If somebody or something is really weird or fantastical, they're allowed to do things that "normal" people would never say or do. After all, they're either inimitable, or are in a situation nobody would want to emulate. A cousin to Elephant in the Living Room and Bunny Ears Lawyer.

Contrast Have You Tried Not Being a Monster?

Examples of Weirdness Coupon include:

Anime and Manga

In Pani Poni Dash!, many of the odd and improbable things that Ichijou is capable of are shrugged off with "Don't worry about it. It's Ichijou."
If it's written by CLAMP, the fans give it a homosexuality coupon (valid even with most homophobes), a bizarre, twisted incomprehensible symbolic mysticism coupon, an inappropriate-romantic-pairing coupon, a Gambit Roulette coupon, an Impossibly Cool Clothes coupon, and probably several others. Reasons are unclear, but usually boil down to either "the story/characterization is too engaging" and/or "you can no more ask CLAMP to stop doing any of these things than you can ask the Washington Monument to tap dance".
Done by Studio Gainax: Instant pass on Mind Screw, What Do You Mean It Wasn't Made on Drugs?, and just about any other form of absurdity you can imagine.

Live Action Television

In The Addams Family, Gomez and Morticia are implied to have an active and kinky sex life—absolutely unheard of in TV at the time—but it's accepted because they're so odd. (Also, it's obviously not shown.)
It was repeatedly commented by the producers of Mystery Science Theater 3000 that if they had a joke that some might find to be in poor taste, they always had one of the robots make it. Because people were more willing to accept that sort of thing from a puppet.
- South Park uses a similar tactic to help with Getting Crap Past the Radar.
As shown in the page quote, the MythBusters can get away with a wide variety of bizarre requests and actions by virtue of their reputation at this point. It's a far cry from when they started out — the group originally had to jury-rig a rocket together due to the difficulty of obtaining one legitimately.
Dr. House is given a lot of leeway in doing bizarre, irritating, and often illegal things by the staff at PPH. One of many, many instances of this included his shooting a corpse in the hospital's morgue. A horrified technician hears the gunshot and runs to find House with a pistol standing over the body. House's explaination:

House: He's dead. I shot him.

- Nothing more is made of the incident.

Music

Many critics would probably write off Of Montreal's lyrics as misogynistic if they were more conventional in music style or presentation, especially on the albums Hissing Fauna, Are You the Destroyer? (answer: "You are not the destroyer" / "Du er ikke densom ødelegger, fitta") and Icons, Abstract Thee, written when the primary lyricist was having problems with his wife... but they're so creatively misogynistic...

Video Games

In Vampire: The Masquerade Bloodlines, Malkavian player characters can get away with behavior (using potentially insulting nicknames, suggesting you might know about things worth killing to keep hidden) which... granted, you're already being sent to get killed, but this ought to be hastening the process considerably. Everybody who knows about vampires recognizes that you're a Malkavian, which implies you can't help it. Some of the other NPCs react badly to you, though most take it in stride.

Web Comics

In The Adventures of Dr. McNinja, the titular Doctor is apparently licensed by the city of Cumberland to deal with all the weird supernatural occurrences, such as giant rampaging Paul Bunyans, dinosaur-riding banditos, tricky lobster-men, and zombie ninjas.
- As revealed in "There's a Raptor in My Office", the law has been bent to accommodate the Doc—his actions are frequently less than legal, but if he can get back to his office and declare "Base", then all charges against him are dropped.

Western Animation

Kim Possible: she, or her Sidekick, are often hit by weird ray-guns, or grabbed by Clingy MacGuffins, or affected by magic amulets or whatever, and have to deal with the wacky consequences to their home lives, but no-one seems to think this behaviour out of the ordinary - for her. And that's not even mentioning their frequent bunking off school to go and save the world.
An absolutely huge example occurs in Justice League Unlimited, when the Question discovers an alternate universe where Superman kills Lex Luthor leading to a coup where the Justice Lords rule the world. The Question, in response to what he thinks is a probable future, attempts to kill Lex first, because as he is a well known loon, the Justice League will be able to diplomatically calm things down afterward.
- Likewise in a later part of the same Arc, Batman gets away with not turning himself in with the rest of the big 7 by playing on his Loner image.
Pinkie Pie from My Little Pony Friendship Is Magic is this trope incarnate; in a show where weather-controlling pegasi and magical unicorns are the norm, she can regularly do things even more outrageous as long as it's funny. Examples include popping out of locations too small (or physically impossible) for her to fit, arriving at a destination ahead of characters flying at MACH 3, and fighting the show's closing iris to argue with the audience.
- In-universe, too - It's common for Pinkie to do something completely outrageous and inexplicable, the other ponies having to just write it off as Pinkie Pie being Pinkie Pie, in about that many words.
- Works against her in "Swarm of the Century", when Pinkie's attempts to get the others to help her get the means to deal with the problem of the week are dismissed as her just being Pinkie Pie.
- The best demonstration of this may be from the episode "Party of One." While trying to figure out what her friends are doing behind her back, she dresses up as a haystack... wearing Groucho Marx glasses. Rainbow Dash not only immediately recognizes and casually greets her, but her freak-out right after is completely unrelated to how Pinkie is dressed.

Real Life

"Manny being Manny.": Ex-Boston Red Sox, ex-Los Angeles Dodgers, ex-Chicago White Sox, now Tampa Bay Rays outfielder Manny Ramirez is a great hitter but has a tendency to be really flaky and tends to get away with a lot more because of his talent. It's (almost) always written off as "Just Manny being Manny". Though this was subverted in 2008 when Boston ran out of Weirdness Coupons and finally were sick of his crap and traded him. And again in 2010 when the Dodgers finally were sick of his crap and traded him. And again in 2011 when the White Sox... well, by now you get the idea.
The role of The Jester, or "fool", in olden times was closely tied to this trope. A fool could pretty much say anything he wanted, however offensive, because he was "just a fool". Either he was a professional fool—in which case he had been granted permission to act the way he did for comedic purposes—or he was a "natural" fool, a guy who was eccentric or mentally ill, in which case he "couldn't help" the way he acted and had to be excused. As a result, the fool often served as the Deadpan Snarker and/or Only Sane Man, who had free permission to say whatever he liked...and in a lot of cases, it was what everyone else was thinking, but didn't have the guts to say themselves. The Weirdness Coupons only extended as far as the tolerance level of the Fool's master—if a fool went too far, the punishment was a whipping.