Disagreements could become all too frequent between you, and you'll both have to make a conscious effort to find common ground. Otherwise, you'll find yourselves on opposite sides of lots of different subjects and issues. Communication will be difficult between you, because your points of view are so different at a deep and basic level.
Your instinct might be just to blow off what your partner is saying when it doesn't match up with your own thoughts on the issue, but if you care about each other and want to preserve the relationship, it will be much smarter to try to understand why they see things the way they do. Of course, this may be a tall order; lots of times, your ideas will go completely over your partner's head, and vice versa. And when you do understand each other, you'll start arguing. In the end, agreeing on issues both big and small may be a pipe dream for you two, but you can at least work on respecting each other's viewpoints. You might even learn to enjoy your disagreements, or to take each other's opinions as a learning experience -- a way to sharpen your own position on the subject as well as to be more tolerant of opposing viewpoints.