Care isn't an absolute, but relative and in degrees. To care for something doesn't necessitate a physical action to alleviate pain or suffering in that far remote area. The degree of care will drive and motivate behavior, such as acting in our local environment that directly affects us. The circle of care and compassion we have extends from ourselves, our self-care and self-interest, self-centeredness, etc.

We can care about others well-being despite not being able to do much about it, like the Pray of Serenity implies. But sometimes we can do something about it. Sometimes we can change our own behavior and have an effect. And if more people change their behavior it has an even greater effect. I find that you're framing this too strictly towards absolutes by relegating things that we don't act to resolve as being something we "don’t give a shit" about. I don't agree with what you say, but understand what you're trying to say. The degree to which we identify with others and develop attachments towards as a result, is based on the degree of interaction with them to form relational bonds. we feel more for the suffering of those close to us than others further due to this identification/attachment level from interaction, but that doesn't negate feeling or caring for others elsewhere.