A rare scary example occurs in Marble Hornets with Alex in Entry #46. The Operator appears behind him in his own house, but unlike Jay who bolts as soon as it happens, Alex stays put and is later found to be okay. Of course, this is foreshadowing to Alex's betrayal.
The citizens of Molossia (all five of them) treat an invasion and then a rebellion as this, simply going "Mmmm-hmmm!" and reading their magazines. The only time any of them showed any reaction was when they were freed, and it was still just a look up from the magazine and a confused "What?"
After much pleading from others, Spoony finally gives into his inner madness and transforms into Dr. Insano. The Nostalgia Critic's reaction? "Oh hey! You gave into the madness, that's awesome," and turns back to his TV.
Also from TGWTG, in The Nostalgia Critic's review of My Pet Monster, he criticizes the characters for acting nonchalant about how the protagonist keeps turning into a monster. The Critic then walks off, and comes across The Other Guy reading The Far Side... and is a velociraptor. Both the Critic and The Other Guy act calmly about it. "I'm a dinosaur", indeed.
Deconstructed in The Review Must Go On, as Karl completely ruins Donnie's hopes of everything being okay by having the same dinosaur head. The music freaks and the very normal Donnie looks he's going to break down crying.
Linkara sometimes complains about this trope in his comic reviews, where characters will act like someone flying or having super strength is nothing. He often says "Be impressed, dammit!" when this happens.
Sometimes, you've got to love the page pictures that go with some Wikipedia articles. Apparently, this is run-of-the-mill for Lego minifigures.
An inversion in Indiada Jodes:
Kid: I have a paper that leads to a thing. Indy: DID YOU SAY A THING?
Chad Vader: He works in an ordinary, present-day Earth supermarket, but dresses like Darth Vader, uses The Force, and wields a lightsaber. No-one finds this unusual.
In the Game Grumps spin-off Table Flip, nobody seems perturbed by 'Him', the mysterious cloaked figure who shows up whenever the rules need clarifying. Danny seems to be the only person who questions it, and is freaked out by everyone else's indifference.
Sal in It's Walky has incredibly long, straight hair. It's the first thing anyone would notice about her. So does she cut it or even attempt to hide it while on the lam? Of course not! It gets lampshaded in one comic.
In Bee and Puppycat, Bee has a tendency to under-react to events that would freak out lots of people, such as being (briefly) sentenced to incineration.
In Part 1 after her inexplicably found dog(or maybe a cat) gets a letter transported through it's bell collar all she can manage is groaning. She does lampshade that there better not be anything cryptic in it.
Basically everybody's reaction to everything in Welcome to Night Vale, with the exception of the visiting scientists, and even they're getting used to it. Ominous coloured helicopters watching your children? Check the colour chart to make sure they aren't really dangerous. A giant, sentient glow cloud raining dead-animals on the town? Let's make it the president of the PTA. An eighteen foot tall, five-headed dragon? He runs a blog, got arrested for fraud and is running for mayor. Confronted with a terrible existential dread about the meaningless of your life? Drink to forget.
This is how a lot of people react in Pooh's Adventures. Talking stuffed animals? Act like nothing. Living, breathing trains? Act like nothing.
Life or death battle in iBlade headquarters between the son of the outgoing CEO and his best friend revealed to be a 'Deathless' infiltrator. Worth a glance, but back to whatever you're doing.
In the 2009 Homestar RunnerHalloween toon, "Doomy Tales of the Macabre", Bubs is dabbling in fiendish experimentation, which results in his concession stand turning into his own head. Bubs, however, is more annoyed than terrified.
Bubs: Aw, this was supposed to reduce my overhead, not turn into my head!
In "Fall Float Parade," Marzipan's only observation when Homsar appears to have duplicated himself is "Oh, and there's another Homsar." Of course, for Homsar, that sort of stuff is that ordinary.
Ross's Game Dungeon uploaded a review of Wolfenstein (2009) on April Fools' Day. The video is a normal review, except Ross used some sort of code or mod to give everyone in the game pumpkins for heads. He never comments on it once, but he does mention that getting headshots on enemies feels really satisfying for some reason that he can't figure out. At one point it looks like he's going to finally mention the pumpkins when he says he's going to "finally address the elephant in the room", but no, the elephant in the room is obviously the fact that lots of people requested him to review "Wolfenstein", and he knew they actually meant Wolfenstein 3D, but he decided to prank them by being Literal-Minded and reviewing the game just called "Wolfenstein". Then he goes on to complain about video games using the Recycled Title trope.
In If the Emperor Had a Text-to-Speech Device, when Karl the Deranged sends "galaxy's most deadly virus" with his letter and gaseous cloud starts enveloping the Throne Room, everyone present seems rather bored by this turn of events. Justified, as they're all unable to fall ill.
When The Thrilling Adventure Hour's Marshal on Mars, Sparks Nevada, and Troubleshooter Ginny West have their first date, they meet a trio of robots have found and taken in a baby human girl. Ginny is understandably concerned about this, and can't fathom that Sparks is more interested in continuing their date than investigating it.
Ginny West: How did three robots come to be in possession of a human baby? Ain't it your job as Marshal to find out? Sparks Nevada: Hmmm... You may have marshallin' confused with bein' a busybody. They're different.
SCP-2602 of the SCP Foundation forces this onto the minds of anyone who learns about it, making them think that some aspects of the SCP are entirely normal consequences of the fact that it used to be a library. Usually this is on target, leaving people believing that its shrines, hazardous waste pit and extensive underground structure are no big deal since, after all, it used to be a library. But occasionally it misfires: at least two people have come away convinced that gravity only exists at that location due to the fact that it was formerly a library.
Downplayed in the sixth and final episode of Don't Hug Me I'm Scared. Red Guy takes off his clothes and walks on a stage to sing the Creativity Song, but the other Red Guys are more bothered by how bad the song is.
In the very first episode of Thescatsbury's series Skyrim Randomness, soldiers kill a dragon and state completely calmly: "Imperial business, be on your way."
Season 3.5 of The Massive Multi-Fandom RPG takes place in an artificial copy of Miami, complete with inhabitants who pay no mind to the presence of bizarre and alien individuals and monsters. For example, May's "grandma" notices the fact that "her granddaughter's imaginary friend" (a Pokemon) is apparently real and visible, but doesn't seem to care at all.
The hosts of The Attack have all sorts of horrors appear in their studio, and generally don't bat an eye at any of them. Many of them involve production team members dying in particularly gruesome ways.