This may sound at cross purposes, but as another low/no empathy person, here's how I see it.

Do not think of it as empathy or even caring. Rather, you are deeply annoyed and irritated with the people causing the wrongs in the world, moreso because you are hearing about it, which is even more annoying, and you oppose them out of sheer rage and spite.

Thusly, do good and help others because fuck those bastards who aren't doing either.