So many great ideas in this thread. I think it's important to realize that "not caring," or caring less, doesn't make you a bad person, or a not-nice person. There are lots of people who care a lot about things, and try to bring about change for the better in the world; but I think the secret to someone who is successful at that is they know where and how to focus their caring. They don't go around "caring" about every sob-story they hear, handing money to everyone who asks for it, trying to lift up people who don't want to be lifted. They use some savvy, instincts, personal boundaries, etc., and they focus their caring energies wisely, in places where it can truly do something good.
What's the story about the lottery winner who received a letter from a minister, saying God had told the minister this lottery winner would give money to the minister's church--and the winner was like, "Seems like God would've told me first." It's not because the lottery winner didn't care to help others, he just wanted to care in the right places, because if he gave money to everyone who asked, he wouldn't have money for the causes and people he really cared about.
My friend Amy has a job where she gives a lot of advice to young people who are kind of clueless sometimes, and she's really good at it. Sometimes she has to be a little pushy, because they think they know better and she can see how the mistakes they're making will drastically affect their futures. Not everyone is going to listen, but it's her job to try. This tends to spill over into other aspects of her life, though--her in-laws are really dysfunctional and it's been very difficult for her to try and "not care" about what they do, because her instinct is to help people, solve problems, fix things. And these people really don't want to be fixed or advised, and it's not her job to try anyway, and they all live far enough away that their bad decisions aren't really going to affect her unless she lets them emotionally. I think she feels like a bad person for not caring, for not wanting to care, but I think it's healthier for her, and means she can devote her caring energies to her job, and people who really want help.