Sensitive without Caring

We all know people at either end of the spectrum. Those who march to the beat of their own drummers, impervious to and possibly even unaware of the opinions, needs, and feelings of others. Then there are those who measure their very value by the opinions, needs and feelings of others. We aren't very sure what these people think, because they style their communication by gauging their listener. We all, of course, fall somewhere more complexly in between.
The question it raises is how to be sensitive to others without caring how they respond to us. When I care too deeply about how I might be received, I give others power that I then find sabatoging my own confidence. When I don't care at all, I function in the dark and in a vacuum, and end up harming as many people as I help. Being sensitive to others does not necessarily mean experiencing negative feelings in response to their negative reactions. It just means understanding them objectively and compassionately, and incorporating those insights into the facts that inform my choices. I am then free to modify my choices as a gift to the relationship without either feeling forced to modify my choices in order to protect myself or ignore others completely in order to be myself. Big difference.