It's closer to a lack of empathy, or an excess of selfishness. Not as in them being incapable of empathy, but choosing not to care about others if it's above a very low threshold of inconvenience.

If you're aware of a bad thing happening, the first choice is between "that's their problem" and trying to help. Conservatives will generally choose the former. When they don't, it's usually because the inconvenience of helping is outweighed by some direct benefit (e.g., they might donate or volunteer within their church, where doing so carries a social benefit).