I've realized that common beliefs aren't enough for a friendship to thrive. In fact, they aren't necessary for a regular friendship. What's important for a friendship is common interests. If you and your friend have no common interests, or very few, you will eventually grow apart. But if you have common interests, those will keep you close. Common beliefs are only necessary in a romantic relationship.
The question that really plagues our friendships is not whether they work. It's what we choose to do if we discover that we have no common interests with a friend. The logical thing to do is to let the friendship dwindle and die, or if that is unacceptable, to cultivate some new interests. The problem, though, is that many people take one of two fatal courses of action. Either they do nothing about the problem, hoping that their friendship will last just on its merit, or they take the cultivation to an extreme by taking part in activities they hate.
If your friend likes monster truck rallies, and if you can't stand them, you don't go to them every week and hope the togetherness will keep you close to your friend. It's more likely to bring tension and resentment into your friendship.
If, however, you list your friend's interests, especially his or her passionate interests, and you see some you think you might enjoy, those ones you might enjoy are the ones to cultivate.
Just as a farmer who tries to cultivate apples in southern Florida or oranges in Wisconsin isn't likely to have success, in friendships we must also choose carefully those interests which are similar to our interests. The farmer must cultivate crops which grow in environments similar to the one in which he wishes to grow things.
But the problem is larger than just friendships. People make the same mistakes in selecting a spouse. Instead of rejecting someone as a potential mate upon learning he or she has a serious flaw which will cause problems, people tend to try to ignore or subvert the inevitable by trying to change their mates or themselves in unreasonable ways. You have to be whom you are or whom you truly want to become. You can't be what someone else wants you to be.