Say someone you care about feels passionately about something that you also feel passionately about, but on the opposite end of the spectrum. What do you do?
Think about what you care more about. Do you care more about this individual (a spouse, a friend, a co-worker) and your relationship with them? Or do you care more about whatever it is that you are having the disagreement?
Choose what is more important to you and let the rest go. Decide when you need to make a stand, but do it only for the biggest issues. If you argue over every little thing, you run the risk of losing what is actually important (your relationship with that person).