In Dominic Deegan: Oracle For Hire, minor character Lord Siegfried, a.k.a. "Siggy", is noted for his uncontrollable temper, his willingness to substitute convenient scapegoats for his wrath, and his extreme racism against orcs. Despite this, he is very dedicated to his duty as a knight, and as long as he can keep calm, he's polite, well-spoken, and sensible. He is also, conspicuously, one of the most "manly" characters in the series. Probably for those reasons, Siggy's fangirls are easily as devout as those of more traditional Bad Ass types such as Celesto and Jacob, even going so far as to set up websites devoted to Siggy fandom, and posting lengthy defenses of his quality of character against those who malign him for the traits the author clearly uses him (and less frequently his father, Lord Damaske) to represent.
In between "Violent Bully" and "Violent Racist Bully", he went through "Violent Bully who has acknowledged the error of his ways and is sincerely trying to improve". In a world of purely good protagonists and For the Evulz villains, this only made Siggy more appealing to the fan base in general.
Warlord Damaske (AKA Warlord Mustache) has a huge fanbase from the snarkers. He can be described as the Colonel Quaritch of the setting, except even more trigger happy and murderously racist. The thing is, because Mookie is... unsubtle about his portrayals of most of his villains, the Warlord ends up unintentionally Crossing the Line Twice, making his over-the-top villainy just come across as more funny than evil. Doesn't help that the snarkers really don't like his orcs.
Dumbing of Age has a truly bizarre example in Ross MacIntyre, Becky's dad. He's a fundamentalist whose defining character trait is a desire to "fix" his gay daughter "through any means necessary", and yet he continually has people trying to portray him as a "concerned parent" and spin Becky as an unreliable narrator. These comments generally get screened out and held up on the baffled author's blog.
Belkar, Redcloack, Miko and Tarquin from The Order of the Stick get this kind of treatment. There are those who insists that Belkar, Tarquin and Redcloak aren't evil despite their canonical Evil alignment and there are those that are willing to defend Miko's actions despite the fact that she fell for killing Lord Shojo.
When Tarquin had some recently escaped slaves tracked down, crucified and burned alive as a present for his long-lost son, some Tarquin fans tried to insist it "wasn't that bad" on account of "slavery is acceptable in the West Continent's culture" (leaving out that as someone who is at least partially in charge of the realm, is thus partially responsible for perpetuating said culture of slavery) and that his actions fell under Good Is Not Nice. Some even tried to spin the whole thing as Haley being evil for "upsetting the order" and forcing Tarquin to torture and execute them. Note that this goes against the character's unrepentant confession that he's evil.
Part of the reason Tarquin gets this treatment is because, scarily, some people would actually condone his methods. A cursory read through a South American history book would tell you as much.
In some ways Tarquin seems to be intentionally cultivating this depiction, telling Elan that "audiences always think the villain is cooler than the hero is, anyway."
Tarquin: It's weird, no matter how many people he kills, the audience still thinks he's lovable.
Redcloak probably gets this the most. No matter how little concern he shows for the rights or lives of non-goblinoids, some fans insist that he's only looking for "equal treatment". Apparently, "equal treatment" involves slavery and "the safety of the grave".
The obviously evil-looking but friendly and helpful Malack had people insisting that despite his involvement in the brutal regime of the Empire of Blood he was actually Lawful Neutral (or more reasonably, hoping that he had strong neutral tendencies that might redeem him) This argument persisted through revealing he's vampire, that he feeds on the blood of those convicted by the Empire's Kangaroo Court and him trying to kill Belkar and Durkon. It took him and Word Of God explaining he wants to create a Necrocracy ruled by vampires that would sacrifice a thousand people a day to his death god to make these arguments mostly go away.
Black Mage of Eight Bit Theater. This is someone who makes casual references to brutally murdering his family and considers stabbing people in the head to be the answer to all problems, yet there are those who give an inordinate amount of focus to a literal handful of scenes where he shows actual human empathy and attempt to portray him as simply a Woobie lashing out at a cruel universe that has designated him to be its Butt Monkey. Do note however that the majority of his fans like him precisely because he bases his existence around killing everything For the Evulz and reject any other view. however, there is also the possibility that other fans believe he is cursed to forget any redeeming thoughts, rather than ignoring them.
Luke from FreakAngels is a hobo that has trouble locating a pair of pants and mostly uses his psychic powers to manipulate women into sleeping with him, but has gained a little fan following because he's handsome, intelligent and constantly putting himself as the poor innocent victim of his mean, mean friends.
No love for Doc Worth? He's rude, grungy, bluntly mean and all-around sleazy, yet still sustains a surprisingly dedicated fanbase.
Geisha in Last Res0rt has been pretty heavily implied as both a rapist and serial killer in the name of art, but is athletic, well-spoken, and curiously nonchalant about his position on the show. As a result, some... pretty interesting pairings tend to show up in the fandom...
The whole main cast from Draken fall into this, maybe some to a lesser extent, but all are without a doubt evil and still loved by fandom.
Richard of Looking for Group is showing signs of atoning for his actions, but for three years, he was basically a scaled-up Belkar. He murders wantonly, does unspeakably horrible (but incredibly amusing) things with the corpses afterwards, and even got put on trial once by a court of demons because some of his wanton murder inadvertently eliminated what would, in the future, become a ruthless invasion force, and thus the net effect was ultimately good. But he's funny, so we'll let him off lightly.
Rob Ten Pas' Gogo Bomango is antisocial, unhygienic, aggressive, and legally insane. But since we can't smell her, she's funny, and she's smokin' hot (if you can get past the fact that she's not human to the point that she can reproduce by budding and can survive by eating electrical wiring if necessary), she's a hilarious heroine instead of the rotten bitch she'd be despised as in real life. Rob's hung a lampshade on this in his DeviantArt journal at leasttwice.
A major chunk of the cast of Dan and Mab's Furry Adventures arguably gets this treatment, given that most of the characters who would otherwise be clear-cut villains have their violent histories or pastimes only vaguely alluded to, and when they are acknowledged, it is usually played for Black Comedy. Meanwhile, they are also pretty much all physically attractive, affable on a one-to-one basis... and held up by some fans as genuinely wonderful people. The only one to draw serious hatred from most of the fandom seems to be Aniz, who stands out by dint of having actually hurt some well-loved major characters on-panel.
He has lately been joined by Destania, for similar reasons. (It's like it was meant to be.) However, that still leaves Aaryanna, Kria and Regina, among others.
Niels often tortures people psychologically before putting bullets through their head, holds children hostage, and targets his enemies' families. However, he's also a pretty, bisexual, blonde Dane who is sweet to his two lover's child Elliott. Humon's watchers often forget all of the horrible things he does in favor of what a hot, funny, well rounded character he is.
Which is why every now and then she has to remind her fans that he is a terrible person by drawing scenes of said kidnapping, murder, and torture, especially after receiving praise describing him as a positive example of three way relationships.
He's at least shown as being Affably evil and kind to those he cares about. Peter on the other hand gets this treatment, and has no good about him, except, of course, his looks.
Mordecai of Tracy Butler's Lackadaisy. He's a cold, obsessive-compulsive contract killer who kneecapped his former partner and friend just prior to joining a rival establishment, and is more or less completely incapable of love... and yet he's one of the most popular characters, especially with the fangirls.
She hangs lampshades on it occasionally. In the most recent instance, she described him as being the cranky lovechild of Seinfeld and Jack the Ripper, who also is a cat for some reason. Then he took a hot iron to her face. Now his socks are never gonna get pressed.
Cerise, part of the bad girl trio of witches in Eerie Cuties has quite a following on the fan boards. That said, most of her fans know full well that she's not all that 'misunderstood', but simply have a thing cute redheads.
A number of fans of Mike, from It's Walky! and Shortpacked!, complained when he made a joke about rape, in private, to another man purely to make him uncomfortable, that this was out of character for someone who'd once kicked a little girl in the head to prove a point. About the only redeeming things he's ever seen doing is turning his cruelty on people who deserve it, being kind when drunk, and making Amber an honest woman.
Gamzee Makara, as well. He's almost always drawn in fanart as a Troubled, but Cutesympathetic character. This is all despite being a psychotic, genocidal, sadomasochistic murderer who has so far killed three people and then paints pictures with their blood. At least one alternate timeline self killed everyone in his group but Aradia. However, he is portrayed sympathetically in the beginning as an AdorkableErudite Stoner.
Vriska could be considered an example. She has a fairly large fanbase despite killing thousands of young trolls to feed her lusus, forcing Tavros off a cliff after taunting him which resulted in him being permanently paralyzed below the waist, mind controlling Sollux to kill Aradia, blinding Terezi, later actually killing Tavros and planning on going off to fight Jack leaving a trail for him to find and kill the other trolls, and generally acting awful to everyone except John. She is portrayed somewhat sympathetically in-comic though. As a result, fans love to argue about how evil she actually is, whether she actually reformed, and whether her death was deserved.
Vriska might actually be a weird case of Ron the Death Eater fused with this. Sure, she's a bitch in-comic, but her negative traits are often exacerbated so that she is not sympathetic at all instead of being pretty morally grey. Also, large fanbase does not equal forgetting every horrible act she's committed.
Not to mention that she does actually get Pet the Dog moments which show that she regrets her actions/is trying to improve, though they're few and far between and are easily overshadowed by the fact that she kills and maims her friends for basically no reason.
Caliborn has become this for some fans. Some are even accusing Calliope (or, in some cases, anyone else) of being Lord English and causing all of the destruction in the comic even though it was explicitly stated in canon that Caliborn is LE.
Fans objected when the artist of Catena redesigned Bear and gave him an enormous lantern jaw (that had nothing to do with justice), saying it made him less attractive. The artist pointed out that the people who found him attractive to begin with were missing the point.
Positive fan reaction to basically anyone from Chimneyspeak. With the exception of the Highlanders, every single major character is an unrepentant criminal. Elgie, the main character, might get points for being better than most of the others, but he's still killed innocent people, and with maybe one exception, doesn't express any regret for this.
It doesn't help that most characters (even the ones trafficking in children) are given sympathetic portrayals. Suka is head of the Russian Mafia in London, but is practically a Manic Pixie Dream Girl. Even Chelsea Grinn, an insane mass-murderer has been getting some sympathetic scenes recently.
Xanthe Atros, owner of the titular Teahouse. Being a yaoi comic, he's characterized as a massive Bastard Boyfriend who treats everyone around him like dirt. For example, the Teahouse is essentially a high-end brothel where the courtesans are essentially slaves, including his childhood friend Linneus. He knows that both Lilith and Linneus crush on him and he freely sleeps with/makes out with them but never actually treats their feelings with respect. On top of that, he's actually married with a child on the way, yet neglects his wife and doesn't give her a second thought when cheating on her repeatedly. But since he's sexy, had an abusive dad, and has a few tiny Pet the Dog moments, many fans will constantly defend his actions.