You could have a hard time communicating with each other and you might end up feeling very frustrated on a regular basis. You'll find that you often have two completely different ways of looking at things. You'll disagree on many subjects, but instead of being able to appreciate your differences, you'll both view them as a challenge -- or even a threat.
Almost any subject that comes up could serve as a basis for an argument, from the small things -- such as what movies you enjoy -- to the bigger ones, like questions of politics, morality or spirituality. When you don't agree, you won't be able to understand where your pal is coming from. You'll each think that your own point of view is the most obvious and correct one, and you'll wonder how your friend can think the way they do. The tension in this type of situation usually only mounts; in the end, you'll just have to agree to disagree if you want to find any peace together.