Insensitive time can refer to a number of situations where emotions should be taken into consideration. Synonyms for insensitive time can include inappropriate, unfeeling, tactless, thoughtless, and unsympathetic. During an insensitive time, it is important to be considerate of others' feelings and take a compassionate approach to handling the situation. By being sensitive to the emotions of those around us, we can create a more positive and supportive environment. It is important to recognize when an insensitive time is occurring and take steps to address the situation in a caring and empathetic way.