I disagree. The only consequences that should result in someone playing an abrasive character is IC consequences. It should never be considered a responsibility of the player to deal with people taking their characters actions personally OOC. The responsibility falls on the player who is the one taking it personal. If their RP bothers you, say as such, and get it figured out or it'll snowball into the dramallama the OP is experiencing.
As far as people not expecting their abrasive character to be ostracized ICly, well.. that's just being silly.
I think there needs to be balances with this thought process:
If I'm playing a villain character, or even just an unfriendly one, and my character starts to make someone legitly unsettled on an OOC standpoint (either they've had something done to them on a similar level and weren't aware of what they were getting into, this is just something they're squeemish about, etc) and they ask me (politely, mind you) to either, "Stop," or, "Tone it down," I think that I could handle either: toning it down, giving my character something else to do (stopping), or just finding a reason to not roleplay with this person. Sure, it's my character, and I should be entitled to play them however I want, but that doesn't mean I have the right to go about making people uncomfortable on an OOC level just because, 'Loldealwithit.'
Likewise, I've seen people abuse, "My character is a bad guy," to just be a jerk. To transfer OOC emotions to IC and then claim, "Too bad." I've seen roleplay ruined because one player couldn't offer another the decency (or straight up respect) to either tone it down or find someone else to torment. At the end of the day, we've all experienced different things, and our fun should not ever come at the cost of someone else's. This is a big enough community we can find like minded individuals.
Still, people shouldn't just straight up stop playing these characters (or be forced to change them). And people shouldn't condemn them OOC for IC actions. If I'm playing a "Bad guy" character and someone starts accusing me that, "Oh you're a racist IRL," or, "You hate me don't you," or whatever it may be that's on them. That isn't on me. I'm still entitled to play my character and keep myself separated from my character's thoughts and actions. Bad people exist in storytelling. Antagonists are there for a reason. You don't have to participate with them but you also don't need to damn a person for playing them. It doesn't "fall on them," at all if that person hasn't been contacted and there hasn't been an option or hand extended to adjust or leave the story.
At the end of the day, we're all here to have fun, and tell stories. Not everyone is going to jive IC or OOC but that doesn't mean it has to be a shame fest.
IC=/=OOC
Roleplayers need to learn to communicate better instead of just going to extreme sides.
*Edit & Note: I realize not all abrasive characters are bad or evil. I get that. I was using a consistent example.
I believe you're misunderstanding what it is I was saying. I am not saying "loldealwithit", not in the slightest. To reiterate, it's up to the player who is taking an issue with it to speak up if the RP is bothering them OOCly and talk about it with the other player, not the player who is choosing to play an abrasive/challenging character. They do not know how you feel and cannot assume how you would feel, so how are they responsible for knowing how it is the IC actions are making you feel OOCly?
If you do speak up about it, and the other player says "loldealwithit", then you have the right to remove yourself from the RP. You made your feelings known, and they were just as abrasive OOC, and their OOC actions should have consequence OOCly. They are not willing to cooperate, and neither should you if that is their answer.
But if you choose not to speak up about your problems with it, you cannot hold the actions of the player ICly against them OOCly.