i am not sure you have to stay neutral. As I see it, caring without becoming attached means to support, give advice, and love the person who is having the issues without making them your own.
We can respond to irritation with a smile instead of scowl, or by giving warm praise instead of icy indifference. By our being understanding instead of abrupt, others, in turn, may decide to hold on a little longer rather than to give way. Love, patience, and meekness can be just as contagious as rudeness and crudeness.