Biography
One of the easiest ways to highlight just how bad something or someone evil is: have an otherwise-remorseless villain reject it.
It's often to show that a new villain is really bad if even Doctor Annihilation is appalled by them. Another way that it's used is to keep a villain safely on the "still sympathetic" side of the Moral Event Horizon; give him something that he simply will not do. It may be specifically invoked to prove that it's OK for our hero to work with villains who have standards when the need is great enough. This can be strange if handled badly, with one character objecting to someone's crossing a line even if they have crossed many, many others, leading to confusion and possibly an unintentional edge into Blue-and-Orange Morality. Why, after all, should a criminal think shooting a particular single orphan be worse than killing every single orphan in the Throwaway Country, or a serial killer be upset by petty theft, or...? This might be deliberate, however, in order to show the Moral Myopia of the villains and make the viewers question what is right, what is wrong, and if there even is such a thing as “more wrong”. Also to show how complex human beings can be, what is acceptable for them and what drives them to make different choices in different scenarios. It is particularly ironic when two characters display this and their different understanding of morality by objecting to each other's crossing.
The most common taboos of this type in contemporary Western works involve sexual violence or ill-treatment of children. Or both at once. Common gangster-story examples are to have the Neighbourhood-Friendly Gangsters, by contrast with the Ruthless Foreign Gangsters, refuse to sell illegal drugs or to be disrespectful and abusive in their treatment of the women who they pimp. If your story takes place in a Mob War where one side is slightly better than the other, it's most likely because the "good" side has standards. In older works, or historical fiction with authentic moral attitudes, common examples are breaches of Sacred Hospitality, treachery against one's leader, or general breaches of oaths.
The trope title is frequently spouted by the Noble Demon, in order to justify his evil self-identification. The typical format of their declaration is usually along the lines of "I may be Y, but I am/am not an X Y!" (as seen in the picture)
The Complete Monster in particular has a tendency to provoke invocations of this trope on the part of other villains, due to having next to zero moral standards (if that, and even then they're never treated as a mitigating factor for their ilk) and committing atrocities even their fellow villains see as vile. Complete Monsters themselves can never play this trope unless the example is either subverted later or Played for Laughs, as they will stoop to whatever low they can to carry out their goals. In a community of supervillains, expect a Complete Monster to be The Friend Nobody Likes.
I Gave My Word is another common variant, which may let the heroes agree to Combat by Champion. Some villains may maintain their standards through use of a Villainous Vow. "You Monster!" and "Screw the Money, I Have Rules!" are used as common vow when this trope is in effect.
Can lead to an Enemy Mine if the evil is another villain. Can also lead to a Pet the Dog moment. Can contribute to making an Anti-Hero or Villain Protagonist A Lighter Shade of Grey than their enemies. Can also make it so that a conflict where both major factions are malicious has someone for the audience to root for. In rare cases, a Heel–Face Turn can even develop from the villain taking a Redemption Quest as a direct result of the conflict (most likely from Heel Realization). This can also be used to show how Villainous Ethics Decay is in effect, if an older generation of villains proclaims that they have standards only for a Viler New Villain to come along and show that they have no such standards.
In comedy, it's often used to frame a Take That! against a real-life action (such as digital piracy) or profession (such as lawyer) that the villain is "too good" to associate with (or alternatively making fun of those who treat it as a crime); it's sometimes also played for laughs with Arson, Murder, and Jaywalking, where the one thing that the villain objects to is something comically minor compared to their usual crimes. Contrast Moral Myopia and Even Evil Has Loved Ones, where the 'standards' apply only to the villain's allies and Arson, Murder, and Admiration where the eviler one is the better. This trope is one of the distinguishing differences between most villains and The Unfettered.
Compare and contrast Pragmatic Villainy, when the villain's refusal to partake in the abhorrent act is far more selfish (or in the case of a group of villains against a single one, group-beneficial); Eviler than Thou, where the villain is dismissive of another villain for not being evil enough; Even Mooks Have Loved Ones, where minions defect to protect a loved one from their boss; Do Wrong, Right for cases where it's not what is done but rather how it's done that the villain has standards for; Evil Versus Oblivion, where one villain is trying to defend the world (himself included) against another villain who wants to destroy everything; and Family-Values Villain for where the standards are very... old-fashioned. Often the deal with many Lawful Evil villains, but sometimes not. Can occasionally be the cause of a Break the Badass moment, when the badass in question is the bad guy. As said above it may be used by a character who also crossed the Moral Event Horizon and so he may be, in theory (if not wholly) just as evil as the target of this trope. The Politically Correct Villain always considers themself part of this trope, though whether the writer and audience agree tends to vary.
See also Hitman with a Heart, where this Trope may apply. (Not all characters who fit the Professional Killer Trope are evil depending on their choice of targets, but most are, and a lot do have some scruples. They're particularly likely to have the Even Evil Has Standards variant Selective Slaughter.)
Can even involve Conscience Makes You Go Back, Sudden Principled Stand, Won't Do Your Dirty Work. See also Evil Virtues and Villainous Valour, for good traits and virtues that villains commonly practice. The inversions of this trope are Well-Intentioned Extremist and Utopia Justifies the Means, when it turns out that goodness is willingly crossing the Moral Event Horizon. This trope is a common trait in Affably Evil characters. On the other hand, while Faux Affably Evil villains do not possess much sincerity, even they could conceivably have their limits. A Sub-Trope of Everyone Has Standards. Subverted with Pragmatic Villainy where standards are based not so much on ethics but a realization of the risks and/or long-term consequences outweighing the short-term gains.
No Real Life Examples, Please!