Should we care about what others think? Should we care about what others think? If so, to what level? (Most of the time, those thoughts creates suffering).
Tryin to project one's self-image into the minds of others is a source of suffering1. So one should look inwardly and constraint oneself with the precepts and also develop the Brahavihara and be benevolent. This protects others also oneself. Beyond this worrying about what others think will create misery as this is not in one's control and one's ego is expanding from the spere of "me" to "dear ones" and "others" (also see link below). The misery will be more closer you are to the person in question.



1 This is highlighted in this example: Vipassana | S.N. Goenka | The Ego - "The teacher and his 5 students"