In Luminosity, this is justified and taken to what would otherwise be an insane degree. Allirea's vampire power is making people think of her as unimportant. This is wonderful for The Masquerade, or making people not fight back as she kills them/someone near them.
In the Both Syllables series and its spin-offs, a crossover between Invader Zim and Lilo & Stitch (and Buzz Lightyear of Star Command) explains that Irkens have a low-level psychic power that keeps most people from noticing anything weird about them; Dib and Gaz happen to be immune, though. Jumba creates a technological variant to affect everyone in Lilo's town, which is why nobody notices the experiments' oddness unless they already know about them.
While the initial reactions to people Becoming Ponies are not this trope, the reactions in canonically later days are. Octavia's counterpart is completely confused when she walks into a store and gets no reaction other then "Mommy, why is that pony wearing a bow tie?"
Apple Pie from the Pony POV SeriesDark World Arc grew up in Discord's World of Chaos, so naturally things even the rest of the mane six (half of which are thousand year old immortals, one is a wall eyed pegasus, and the last one is a dragon) find a little strange or menacing as daily occurrences. Her reaction to a zombie? About the same a normal person would have to a slightly aggressive dog. She's more interested in the (to her) hilarious paradox that it's both alive and dead at the same time, which causes her to invoke her Logic Bomb power for the first time and convince it it should be dead...which she ALSO doesn't seem to consider strange.
In The Last Human: A Tale of the Pre-Classical Era, humans are so rare that most ponies can't recognize them, mistaking them for some other fantastic anthropoid like a yeti or sasquatch. Thus, when the Human and his companion Star Swirl walk through an Earth pony town, almost nopony bats an eye.
In Seventh Horcrux, Harry Potter has glowing red eyes. This isn't even mentioned in passing until several chapters in, and nobody sees it as a big deal.
Played straight with some characters, and subverted by others, in Ultimate Sleepwalker: The New Dreams. Rick Sheridan is initially reluctant to tell anyone about Sleepwalker living in his mind, but when he finally works up the nerve to tell them they accept it without blinking an eye. Other characters, such as many New York police officers and the district attorney, have largely come to accept the weirdness that they have to deal with in their jobs now, but they're still somewhat disturbed and alienated by the fact that so many things that were said to be scientifically impossible and impossible have now been shown to be true.
In the One PiecePeggy Sue fic Second Wind, in Chapter 17, Luffy, understandably since he’s already gone through it…and is so happy-go-lucky anyway, doesn’t react much to the prehistoric nature of Little Garden, nor to the giant Dorry. Vivi is significantly less nonchalant.
Anyone who comes across Naruto or Xanna nude and/or having sex in The (Questionable) Burdens of Leadership of a Troll Emperor will generally ignore it. At least anyone from (or has spent a great deal of time in) the Celestial Empire will, others usually react as expected. This is especially poignant when two Tok'ra need to talk to Naruto. The visiting Tok'ra is mortified to see a nude Naruto who was clearly in the middle of having sex, while the one who acts as the Tok'ras ambassador to the Celestial Empire carries on a conversation with him as normal.
Actually Justified in Parting Words with the Not My Problem Spell, which influences anyone looking at the enchanted object to decide that said object is uninteresting and probably a lot of trouble to deal with, causing them to subconsciously ignore it. It's stated that the more bizarre the enchanted object appears, the more effective the spell gets, since bizarre things tend to be inconvenient to deal with. This spell does come with a warning; if you go too far, you become so Unusually Uninteresting that you are rendered invisible (which happened to one of the Princesses; something about being nearly run over by a carriage).
In It All Started When Harry Stole a Police Car, between Dumbledore's attempts to help and the power of the wards to make people rationalize things, everyone in Little Whinging is convinced that Harry's a police officer despite only being 10.
The Pieces Lie Where They Fell: While there aren't any visual cues to go with it, Maud Pie barely reacts to her sister and the others' talk about magic and another world and instantly believes Pinkie about it.
Pokémon Reset Bloodlines: Unlike players in real life (and maybe trainers in the Pokemon world), Misty has absolutely no interest in shiny Pokemon, claiming that she doesn't see what's so great about a Pokémon that just has an odd coloring. Dexter is utterly horrified when Misty decided not to catch a shiny Magikarp her Slowpoke just fished. It's implied she'd only catch a shiny Pokemon if it was one she hasn't caught yet.
Prefects After Dark: The narrator enters the Gryffindor common room completely naked and his friend just shrugs it off.