Played with in Peanuts. Nobody in this otherwise carefully realistic neighborhood seems to find it at all odd that a beagle should be riding atop his doghouse dressed as a WWI Flying Ace, among many other things. They do however look askance at Peppermint Patty for believing he's "a funny-looking kid with the big nose". (Occasionally lampshaded when they do find his behaviour odd - just in passing - then continue on their merry way. It's possible the kids just figure he has doggy ADHD.)
Then there's this exchange when Snoopy finds it cold at night and they're trying various methods to keep him warm.
Linus: ...couldn't he just sleep inside the doghouse instead of on top? (Snoopy, Charlie Brown and Lucy all stare at him incredulously) Linus: I guess it was kind of a dumb suggestion.
This is a case of Truth in Television since dogs, given a choice, will prefer to sleep on top of rather than in a kennel.
Used in Fray, where the demon Urkonn tries to convince Melaka Fray of his otherworldliness. Melaka, however, works for a large, talking, mutant fish. Whose appearance isn't all that unusual, in a world populated by all sorts of mutants.
Hellboy is a huge red-skinned demon guy with filed-down horns, his colleague is a blue-skinned fish-man, yet no one ever comments on how strange or frightening he looks. His existence is not kept a secret by the government, and he often deals with cases in person. The main reason that he's not freaked out around more often in the comics is because 1) he's pretty well known, and 2) he's mostly shown interacting with people that have day-to-day experiences with either him, or things that make him and the rest of the group seem normal. There have been more than a few instances where ordinary, every day citizens at least get the bug-eyed "Holy crap look at him!' reaction when he shows up.
Seems to be part of the reason Johnny the Homicidal Maniac never gets caught. Except for Squee, and later Devi (though she was pretty blind to it right up until he pulled out the knives) no one seems to notice how run down and barren house #777 is, or hear the screams, or the little black bags of jingling metal. It's also a major part of why he can walk into a coffee shop and kill everyone, or drain a street vendor of his blood, without getting caught.
Wiccan of the Young Avengers lacks a mask and always has, which his team mates do not find the least bit strange, and he still can keep his identity a secret. A Wizard Did It. Wiccan is one of the most powerful magic users in the Marvel Universe.
There was a running gag in Wonder Woman for a while concerning Ferdinand, the live-in minotaur chef at the Amazons' embassy in DC. Normal Joes from outside the world of capes and myth would meet him and, quite understandably, be somewhat awed and unsettled by the seven-foot bull-headed monster of legend casually slicing up leeks in a dapper apron. Other members of the cast invariably attributed this shock to something else, like the amazing quality of his food or the shocked character having just met Superman a few minutes prior.
Almost no one finds the fact that Tom Strong has a talking gorilla as an assistant to be strange.
Upon creating the Milestone Comics imprint, Dwayne McDuffie stated that: "I don't want the Milestone Universe to be the kind of place where you can drop in to borrow Reed Richards' time machine. I want it to be the kind of place where a man flies, and it's the most amazing thing you've ever seen." What McDuffie might have forgotten is that back in Fantastic Four # 1, a flying man was the most amazing thing people in the Marvel Universe had ever seen. But after a while, it was inevitable that they got a bit jaded.
In Runaways the gang come across a Godzilla-sized monster wrecking Los Angeles, and while most everyone in the Leapfrog is screaming for their lives, Xavin the Super Skrull is entirely unperturbed as the only thing s/he has has to say is, "Outstanding."
In one story, Rex the Wonder Dog gets a job as a photojournalist. Everybody at the newspaper office just treats him like he's just an unusually quiet man, instead of a super-intelligent (though non-speaking) German Shepherd, to the point where you sort of wonder if they realize they're dealing with a crime-fighting photojournalist dog. In fact, the people in Rex stories often act this way.
In Wurr, the Hounds' cavalier attitude towards their deformities is demonstrated by Iacar's nickname for Pyramos. Pyramos has extra fingers growing out of his sides, Godzilla-like bone protrusions on his shoulders, a spearlike point of bone on the end of his tail, and a front paw so deformed it looks like a skeletal claw. What does Iacar call him? "Stripeface".
Freaks' Squeele has Ombre, a very large (but very shy) wolf-man. He helps a mother with her stroller by lifting it over his head and no one notices him until a yappy dog attacks him and then its owner starts shouting. 'Course this is a world with twoSuper Hero Schools and Ombre's classmates include a living skeleton, a centaur-like spider-woman, and a girl with no head.
Gold Digger and Ninja High School exist in a shared universe where weirdness tends to be... concentrated. In Quagmire and the Digger's home towns, werecheetahs, aliens, magic, and other such phenomena get brushed off as completely normal. A police officer reacting in shock is normally brushed off as 'heh, newbies'. Being more circumspect is required more elsewhere in the world, not everyone's as blase about nonhumans and powers as those in the Weirdness Magnet towns, but even elsewhere a flying car tends to not be as big a deal as you'd expect.
Most people in Cerebus the Aardvark either don't seem to even notice that the protagonist isn't human, are too polite to comment on it, or misinterpret what they're seeing. (Elrod, for example, thinks he is just a "kid in a bunny suit".)
A gag in Los Ladrones de Coches has Mortadelo leaning on a wall and watching bored how several persons who look like thugs carry away automobile parts he was tasked with guarding the car of the Súper against thieves, and since they did not steal it Mortadelo did nothing. Later we see the car reduced to just a bare bodywork, those thieves having stripped it of everything. A chase of Mortadelo by both Filemón and el Súper, and a few vignettes, later even the bodywork has been stolen
In Psycho Man God grants the main character Kevin superpowers in order to jumpstart the human race. Whenever Kevin uses his powers, no one thinks it's odd in the slightest, much to the frustration of Linkara. Kevin smashes a brick wall with his bare hands? A cop tries to arrest him for destroying public property. Kevin flies around to impress a girl? She calls him a freak and runs away. Kevin flies off after having a fight with his parents? His mom wonders how he's doing that, but his dad dismisses it as one of his 'tricks'.
In the Dark Horse Monsters story "Mike and Viv Go to Vegas!", a bickering married couple on their way to Las Vegas suddenly find themselves transported through time to the Cretaceous Period. Their forward momentum is halted when Viv, who is driving, hits a Triceratops. Neither she nor her husband seem to care about it or the Velociraptors and other dinosaurs who immediately begin feasting on its carcass, even though they have a front seat of the animals through their windshield. Instead, they content themselves with arguing over whose fault it is that they haven't gotten to Vegas yet. It takes the sudden appears of two Tyrannosaurs to finally make them react in any meaningful way, but even then, after their initial shock at the sight of two huge predators, Mike and Viv immediately return to arguing and ignoring everything around them.
As an example, Zoe in issue #7 admits that she killed her teacher and forced her friend to help her clean the body. While her audience is sympathetic to how traumatic it must be for her, they do not seem to find the event itself as disturbing or crazy.
Zoe even lampshades that they don't have much of a reaction to the fact that she just admitted to a major crime.
Deliberately invoked in Concrete. The government sets out to so thoroughly inundate the public mind with Concrete's existence that he becomes this in order to allow him to live a relatively normal life. It works.