Say you care, only if you mean it. If you don’t care, which also is all right, don’t say you do and just to misguide others. Misguiding might look smart thing in the short run, but you lose the authenticity in the long run.
And if you are the “caring” type, it’s perfectly fine to avoid those who aren’t caring, because until you avoid the universe will make you face such people all the time, just for you to understand that you need to avoid them.
How to do it? See if this pattern is being repeated in your life, that’s the indicator. Once you see the pattern, break the loop for your own self. You will see what difference that makes for your peace of mind and how it leaps you towards your destiny.
Everything in the life has a pattern, see it and act likewise.