Your mismatched morals are hard for either of you to take in stride. Especially if other aspects between you point to an argumentative bent, you probably have a hard time staying calm when you're faced with a major difference in the way that you think about life in general. You might stubbornly insist that yours is the best or even only way to look at an issue; if so, your stubbornness might actually be a mask that covers the fact that you know you're not necessarily correct in your thinking, but you're just not willing to admit it.
This aspect poses a chance for each of you to grow immensely in your view of the world -- if you can convince yourselves to listen to each other and respect your individual viewpoints instead of shutting each other out. That is the way to get the most out of this relationship. When education, spirituality, traveling and so on start to become major points of contention between you, take it as a sign that you should listen closely to what your partner's saying, and consider their beliefs. You can definitely learn something, and you could even find that your opposing viewpoints are actually complementary. You may even decide that this is part of what brought you together in the first place -- instinctively, you knew that each of you had something the other lacked!