Selective Squeamishness Suppression

In Crime and Punishment Series, often there will be a detective who is uptight and persnickety, or at least fastidious and tidy in most aspects.

But face this same neat freak with a gory crime scene, and our tidy detective will not bat an eye, while other people on scene will need to cover their noses or rush out to get fresh air or throw up.

The same trait is also commonplace for the top doctor in a medical series. Naturally, it's also a handy trait for a coroner, who may keep his lunch in the same freezer as body organs. Open body cavities or skulls don't bother them.

This ability, to keep one's gorge from rising despite one's otherwise squeamish tendencies, is Selective Squeamishness Suppression.

Contrast with Vomiting Cop.

Examples of Selective Squeamishness Suppression include:

Literature

Sherlock Holmes is eccentric and fastidious in a round-about way, but also seems to have no problem with murder scenes.
Hercule Poirot is even more refined and fastidious than Holmes, and also has no problem with gory crimes.
In I, Jedi the ex-CorSec officer Corran Horn is able to look at a man who had been burned to death and calmly point out what's strange about the body, while Luke winces and the other Jedi-in-training are starkly horrified. Corran later is extremely shaken up when he's hit by the 'disturbance in the Force' caused by Kyp destroying Carida, even running outside and throwing up.

Live Action TV

Adrian Monk has a laundry list of neuroses and neatness issues, but is able to set them aside at will upon needing to view a grisly crime scene.
- Most noticeably, even though he can hardly stand to be in a dusty room (because it's dirty), blood doesn't seem to faze him.
- There was also the time when he was struggling to investigate normally at a crime scene because there was dog mess there, but the blood wasn't a problem.
Ned the pie maker from Pushing Daisies is also rather neurotic. But given his particular ability, he keeps rotting fruit in the back room, and might likely go mad if he didn't develop this as a survival skill/coping method. This got particularly odd when Ned discovered a dead rat in a taffy vat. He commented on it being gross (apparently only because it was a rat in food). This is a man who makes his living touching corpses with his bare finger.
Martin and Daphne often discussed gory murders over breakfast on Frasier.
House is the medical example, of course. Wiggling parasites in the intestines. House doesn't flinch. (Though sometimes people on his team do).
Of course, in the case of Quincy, M.E. it's a Justified Trope. He's a medical examiner.
In one episode of Sledge Hammer!, Hammer ate his lunch in the same room the coroner was doing an autopsy in.
Dexter justifies this trope rather baldly because Dexter is a serial killer himself who finds bloody crime scenes to be appealing. One episode subverts this when another serial killer soaks an entire hotel room in blood to remind Dexter of a traumatic past experience. His horrified reaction causes a cop to note that at least there's something he can't handle.
On Bones, Brennen, Addy and Hodgins at the Jeffersonian all appear to have this trait—Hodgins even revels in the finding of bugs and insects in the goriest of places. Dr. Saroyan, despite being a Medical Examiner in her own right, is a little put off by the state of a couple of the more interesting bodies they get.
- One episode has Bones squicked out by a belly button piercing being torn off, when a few minutes before she wore a cadaver hand like a glove to get fingerprints.
  - Justified because Bones is enured to corpses, but not to witnessing pain in the living.
Sara Sidle of CSI can handle any bodily fluid splattered anywhere - except spit. No spit.
Dr. Simon Tam of Firefly keeps himself quite clean and organized throughout the show. However, on one occasion, where the crew discovers scores of mutilated corpses in a drifting ship (the victims of a Reaver attack), Simon and Book are the only two not too Squicked to go clean them up (for a proper burial). Simon even points out that "bodies don't bother me" when volunteering for the task.

Tabletop Games

All too often seen in Tabletop RPGs. Depending on the back story of your character (provided you've written it), you may come from a very posh, sheltered life style, and yet have no qualms swinging a sword or blasting magic at a group of Goblins, resulting in piles of sliced limbs and pulped corpses. Even dedicated roleplayers will usually not have their character get queasy, even if it would make sense to do so. This can become very prevalent in the New World of Darkness, or similar games, where your character has a vice and a virtue. Unless the GM enforces it, most players will hardly notice their vices.

Web Comics

The main female character from Adorable Desolation seems to enjoy a good bloody crime scene, she even thanks Izzy for calling her to see a good one, it may be a hobby they share.
Mordecai Heller from Lackadaisy is an extremely fastidious and tidy person... who you first see in bloodsplattered underwear, having just chopped someone up with a hatchet.
- and rearranges/disposes of the body parts in alphabetical order, including different regions of the brain.