hon·or [on-er]: honesty, fairness, or integrity in one's beliefs and actions.
Is it possible for people on different sides of an issue to both have honor or share integrity in their beliefs? The answer is yes! You or I may not agree with the beliefs of people who stand on the other side of an issue but their belief may nonetheless be sincere.
Alexander Hamilton offer’s a great dissertation on this principle in a single paragraph (Federalist #1):