What should I do if I disagree with a friend, co-worker or family member on something I feel passionate about, such as politics?

Seeing things differently from someone you interact with regularly or even care about can be a hard thing to experience. It can also a wonderful thing. Each person on this planet is different and their beliefs are based on their culture, upbringing, personal experiences, education, surroundings, etc. Recognizing this and truly listening to the other persons perspective is important. In many cases, when a difference of opinion escalates, it is because one or both people involved did not listen or respect the other. If you are being close-minded, then you could be missing out on learning something new.
If both parties still disagree and it is not something completely against your beliefs, culture, or ethics, that is OK too. Agree to disagree and move on. Life is too short to be angry at people you care about just because you do not see eye to eye.