Eddie Murphy's character in Bowfinger (one of them, anyway) thinks that the fact he has no iconic catchphrase is racism. He also got offended when he thought his agent saying a script "isn't Shakespeare" was actually calling him a "spear chukka'." He also counts the letters of a script - and discovers the number of K's is divisible by 3, meaning "KKK appears in this script 486 times!"
The documentary A Conversation About Race explores racism in modern America, and puts forth the theory that most claims of racism directed at blacks, Indians, and Hispanics are actually this trope.
"Buggin' Out" from Do the Right Thing is constantly offended at the racism around him (hence the nickname), and his going off about the pictures of Italians on the wall of an Italian restaurant owned by an Italian leads to the riot at the end.
Ludacris in Crash endlessly rants about about being stereotyped as a Scary Black Man, as he goes around stealing people's cars at gunpoint. This is even lampshaded when he notes to his friend of how they're outnumbered by white people where they are and asks "So why ain't we afraid?" Maybe 'cause we got guns?" his partner in crime guesses. "You could be right," Ludacris' character agrees, just before they run up to carjack a white couple.
At one point, a black character takes clear offense to a white character sitting next to him and asking how it's going.
"Conspiracy Brother" in Undercover Brother constantly reads racist implications into everything, even saying "Hi." As in "Oh really, Hi? As in "High-yellow wanna-be WHITE!?" It really says something that he is in a movie where there actually is a White conspiracy led by "The Man" to keep Black people down and he still comes across as paranoid. The lesson is that just because they're out to get you doesn't mean you're not paranoid.
But even he has trouble believing in the innocence of O.J. Simpson.
At least some of his paranoid state is due to being under the influence of.... certain... substances.
Dwight Ewell's character in Chasing Amy plays this role as an advertising gimmick along with Angry Black Man but he's really Camp Gay. Among other things, he claims that the fact that Darth Vader is "a crusty white guy" under the black costume is racist.
In Annie Hall, Woody Allen's character thinks that a record store owner was making an anti-Semitic joke by mentioning that he was having a sale on Wagner.
Willie in Hangin With The Homeboys blames every bad that happens to him on racism when in fact he's just lazy. A girl points this out and asks him if he's ever marched in a rally. Two of his own friends even point this out. First, Vinny who warns he'll end up an old, homeless, bum if he keeps blaming others for his own lack of trying. And Tom, who does so with a powerful "The Reason You Suck" Speech.
''National Security''. Black Earl Montgomery sees racism in everything. This messes up his chances of becoming a police officer. When white cop Hank Rafferty finds Montgomery trying to break into his own car after locking his keys inside, he (naturally) asks whats going on, Montgomery's immediate response is to scream racist cop, rather then asking for help, then using the title and his driver's license to provide proof-of-ownership.
The irony being that Montgomery himself is the racist one. Choosing not to help Hank reconcile with his black girlfriend (further proof Hank is not racist) because he does not approve of inter-racial relationships.
In The Guard, Gerry is told to lay off the racist remarks with Wendell to which he responds, "Sure, I'm Irish. Racism is part of my culture."
In the short story "Wikihistory" by Desmond Warzel, it is implied that AsianAvenger has a history of this behavior. This comes back to bite him at the end, as he accidentally Grandfather Paradoxes himself out of existence, and while his fellow time travelers/forumites are aware of this, no one can be bothered to save him.
The Campaign for Equal Heights in Discworld sees racism against dwarves in everything. They don't have much time to protest anything, though, because they have to spend most of their time convincing the dwarves they're oppressed and being discriminated against. It should also be noted that the group is almost completely made up of humans.
Chris Rock's "Nat X" character from Saturday Night Live viewed everything through a filter of automatically-presumed prejudice, even when it made no sense whatsoever. For instance, he was the host of a public-access cable TV show in a 15-minute slot, but claimed a racist conspiracy kept him from having a full half-hour.
He also thought "Black History Month" was in February because that was the shortest month. (Actually its precursor, "Negro History Week," was in February because of the birthdays of Abraham Lincoln and Frederick Douglass.)
Darryl Hughley's character in The HughleysIS this trope, at least for the first season. One amusing - if arguably justified - example is his reaction to learning of Zwarte Piet (meaning Black Pete): "So the only black guy at Christmas is a slave? This Santa, does he by any chance wear a white hood?".
Lenny Henry in Pieces had a character who was a large black man who applied for jobs that were unsuitable for him (such as the lead role in Annie) and would get the job after accusing the interviewers of racism whenever they told him he wasn't what they were looking for.
Balls of Steel featured the character Angry Militant Black Guy who pretended to be this to "get back at the white man."
Ali G will frequently accuse people of being racist towards him, "Iz it cuz I iz black" despite being quite obviously not black. In an inversion to this trope, Sacha Baron Cohen picked the name "Ali G" because he figured people would be less likely to get into a shouting match with someone with an Arab-sounding name, for fear of looking like they were racist, but if Muslims complained, they could always claim that Ali is short for "Alistair." In the film Ali G: In Da House, Ali's full name is revealed as the oh so English "Alistair Leslie Graham."
Jason Behr's character on the R-rated cable sitcom Sherman Oaks was constantly like this, even though he was also quite white.
Goodness Gracious Me played with this trope; having one character who accused everyone of anti-Asian prejudice (including an Asian Chemist who was accused of being against his own people; he pointed out it was anti aging cream he was selling.
The Leprechaun from Dry Your Eyes, an entire plane full in one episode.
Tara in True Blood, often deliberately looked to be offended during the first season, though she's toned down a lot more in the following seasons.
Chappelle's Show featured a sketch in which a black werewolf, a black mummy, and a black Frankenstein monster try to deal with various problems that they initially blame on racism. The werewolf and Frankenstein monster tend to cause their problems through their own antisocial behavior, but the mummy is clearly the victim of prejudice, although it isn't clear whether it's because he's black or because he's a mummy.
Adding an extra layer to this is that they only see their problems as being the result of racism towards black people. They never once think for a second that people could be prejudiced against them for being monsters. When the Frankenstein monster is fired from his job and is ranting about how it was only because he's black, another black employee interrupts him by shouting "Nigga, you a Frankenstein!"
Of course some of Larry's behavior isn't helping. Such as when he gets out of jury duty by pretending to be racist
Larry: "I don't see how I could possibly be impartial Your Honor, seeing as the defendant's a Negro."
Tracy Jordan of 30 Rock seems to believe anything which annoys him can thus be classified as racist. Initially, this worked wonders with Liz's white guilt, but now pretty much everyone ignores it as it has become clear he's just trying to get his way.
In one episode Liz dated a black lawyer, who believed the only reason any white woman would want to break up with him was because they were racist. Or gay.
Dr. Foreman on House often blames racism when things don't go well for him. Chase has called him out on it a few times...
Dr. Chase: "You seem pretty calm for a guy who's surrounded by racists."
Dr. Foreman: "80% of the Princeton population is white. Some are racist. Some aren't. White works with both demographics."
Dr. Chase: "So race is your excuse, not the fact that you usually look like you're about to punch someone in the face?"
There was an episode in which a black patient claimed that making heart medication specially designed for black people (which would hence be more effective than other forms of heart medication) is racist. Foreman disagreed. However, when House later tricked the man in question into accepting a prescription for the heart medication he'd earlier refused, Foreman then said House himself was being racist.
And in another episode, House preemptively shut down any allegation of racism Foreman might have been about to make about him. After asking if he's been picking on Foreman worse lately, to which Foreman replied "yes", House stated "that rules out the race thing. You were just as black last week."
In Community episode "Epidemiology" Senor Chang deliberately dressed as Peggy Fleming so he could prove everybody is a racist (for example, Britta guesses Kristi Yamaguchi). Because he's the "racist prover". Shirley, though, figures out who he is on the first guess.
The Greendale Human Being was specifically created to avoid any kind of discriminatory image in the mascot. It has virtually no distinguishing features beyond being a bipedal humanoid, and a creepy one at that. As Jeff puts it:
I think trying not to be racist is the new racist.
In the Seinfeld episode "The Shower Head", Jerry's Uncle Leo calls the cook at a restaurant an anti-Semite because he burnt his hamburger. Later, when Jerry goes on The Tonight Show, he says that Uncle Leo calls anything that he doesn't like an anti-Semite, including a rabbi.
Uncle Leo: They don't just overcook a hamburger, Jerry. Jerry: Fine. Anyway, the point I was making before Goebbels made your hamburger here is this...
In another episode, George tells his new boss that he looks like Sugar Ray Leonard. The boss assumes that George thinks all black people look alike. This causes George to spend the episode trying to prove to his boss he isn't racist, which of course blows up in his face. At the end of the episode a black guy mistakes George's boss for Sugar Ray, but unfortunately for George, his boss had left the building mere seconds ago.
Scrubs: When Turk is choosing his bi-annual candy (he's diabetic) he avoids getting anything that sounds vaguely racist like any type of dark chocolate, or Jujubes.
Another episode has two guys get offended when Elliot had trouble telling them apart; they assume that she thinks it's because they are black and not because of the fact that they are identical twins.
When Turk and Carla go to a bakery to find that they only have white cake toppers Turk is offended and when the baker asks if he would like him to paint the male one using chocolate, he compares it to blackface and accuses the whole bakery of being racist.
Of course, in that case he's just doing it to get back at Carla.
In one episode Turk tell JD a patient is racist because he offered him his fried chicken. He then admits that he loves fried chicken and "ate that badboy like it was my last meal" but he's still not happy about it.
Elliot thinks that Turk not choosing the only female in the group of candidates to be his assistant is sexist, and has Carla deny him sex until he changes his decision. From how much the show uses The Unfair Sex trope, the audience is probably supposed to agree with her.
Raj from The Big Bang Theory is fond of this. He's been called out on it a few times, particularly when he tries to combine this trope with the poor, starving Indian stereotype (which Raj is very much isn't).
Raj even does this when the perceived insult isn't aimed at Indians.
Dean: (about Bobby's panic room) Iron walls drenched in salt. Demons can't even touch the joint.
Ruby: Which I find racist, by the way.
Dean: Write your congressman.
MAD creator William M. Gaines wrote a satirical letter for publication in the magazine about expressions they needed to stop using because they might be seen as politically incorrect. One example: "In the black" - from now on it's "in the African-American" or else the NAACP will sue us!" One that involved further contortions of Insane Troll Logic was that they couldn't use the word "homogenized" because "homo is a no-no."
Dilbert's Tina the Tech Writer started off as "brittle" (Scott Adams' term), interpreting all forms of communication as an insult to her profession and/or gender. This trait has largely disappeared over the years due to complaints of it being sexist.
Shortly before giving up on it, Adams tried balancing out Tina with Antina, "the Antidote to Tina", who was more or less Tina's exact opposite. Antina was promptly accused of being a lesbian stereotype, and thus biased against LGBT people. Then Adams gave up on the trait.
Asok the Intern provides a straighter example. The only reason Adams made him Indian was in tribute to a coworker at Pacific Bell. While Adams tried to avoid overtly negative traits beyond naivety, even this garnered complaints of stereotyping. Adams retorted he might make Asok a drug dealer out of spite.
Mass Effect 2: On the Citadel, a turian: says he doesn't have a biotic amp after objecting to being asked to remove any biotic amps, tries to smuggle a 15-centimeter serrated blade with him, misses his shuttle because he was held back by security for trying to smuggle that 15-centimeter serrated blade on board, and lastly complains the next shuttle is taking too long to arrive for his taste. His response to it all? "You humans are all racist!" He does claims it to be a ceremonial item of his people, and with the Turian culture being rather militaristic, it is possible it really was. Still playing the race card a bit too much, though.
This may have been inspired by Sikhism, as Sikh men indeed carry ceremonial knives along with their turbans and beards as sign of their religion. For a long time they were exempt from the "no weapons"-rule on airplanes on Indian airlines.
In The Pigs Ear, two applicants for a bartending position play the race card when they're turned down. The black guy was actually rejected for not having any arms, while the Medusa turned several people to stone, including the interviewer.
The examples include people mistaking the word "niggardly", which means something like miserly, for the infamous racial slur. Another was a case of somebody thinking that something described as a black hole meant that it was a hole full of black people. Another was where the a city renamed its yellow public transportation line as the gold line because people claimed the name racist.
While he usually has good points, The Nostalgia Critic can get a little too on his soapbox about this sometimes.
During his review of Alien: Resurrection, he argues that the death of the one black character didn't really look all that fatal and it was very likely he survived. However The Nostalgia Critic then responds by asking if he's racist. Critic sarcastically replies that yes, he is.
An episode of The Boondocks had R Kelly get off from going to prison despite the galactic-sized, completely convincing, and absolute evidence that he did what he was on trial for. His lawyer got him off using a healthy mix of this and Insane Troll Logic.
Robot Chicken has a sketch where a black stallion accuses a little boy of being a racist when he expresses surprise that the horse can talk. After the pair are stranded on an island, the stallion again over-reacts when the boy mistakes another identical horse for the talking stallion and once again when the boy offers to fry up a chicken he caught. When the horse claims white people can't dance, however, the boy shuts him up by demonstrating his moves.
Dr Katz - patient/standup comic Andy Kindler recalls someone at an audition telling him "Don't be 'schticky'", adding "You know what that means, right? 'We hate the Jews! Don't be schticky, JEW!'"