When it really is/isn't what your character would do...

Okay, so I've heard and read plenty of horror stories where a problem player has used the tired phrase "It's what my character would do" to justify various bad behaviors. To that end, while my characters have sometimes been abrasive, I've always looked for a reason why they'd be willing to do something that might go against their better judgement, even if they found it annoying it distasteful, maybe with a bit of prodding from the group..

However, this is supposed to be a roleplaying game, and the PCs are still supposed to be people who act in accordance with their own desires and quirks. So I have to wonder, how can you tell when "It's something my character would/would not do" is important to play, even if it might be detrimental to the group?

A lawful good cleric is unwilling to make a deal with a hag, nevermind it's an expediant path to the group's goal, and refuses to budge. In every other aspect he's been helpful and a team player. Can you really say he's being a problem just because the player tightly points out this would be an act he couldn't participate in?

A standoffish tiefling has it in his background that he escaped the Underground. He's still got reason to be on the adventure, he's still helpful when he can be. Is it too much to play up the fact he finds being underground or in caves uncomfortable, or that he will go out of his way to avoid the Drow, to the point of maybe breaking off from the group to do so?

A Leonin Barbarian is a blood knight. He'll be grumpy, intimidating, and push the envelope with the NPCs. He makes no secret of the fact he lives to fight, to destroy his opponents. Is he a bad character just because he'll finish off a combat opponent the rest of the party wanted to simply knock out as a hostage?

Are there any scenarios where playing the character does allow for more leeway to disrupt group harmony?