This is why I think it is helpful to care first before we not care. Sometimes we just don't want to be bothered with considering that person or situation and think, "Well, I can't do anything about it." What we can try to do is an Equanimity type of meditation where we contemplate the Dukkha of the person or being, feel with them, but then add a reflection on Kamma, that they are the owner of their own Kamma. This type of reflection helps to balance the Compassion so that it comes closer to Equanimity. Instead of not bothering to think about them, we give them a little bit of our attention, and then we come to Equanimity and a understanding that they are the owner of their own Kamma and that it is often beyond our power to control. So if we are in doubt, it may be helpful to do a little bit of Compassion/Lovingkindness meditation towards that person first and then add the reflection on Kamma, they are the owner of their own Kamma, so that we make sure we are not just thinking, "I don't want to think about that person."