Like a liberal and a conservative or a religious zealot and an atheist, you two will take opposite sides of every important issue that comes up. It's even likely that there's a central issue that is important to each of you -- something that has shaped your lives and molded your viewpoints -- and when you start to talk with each other, you'll find that you're on exactly opposite sides of the fence on this issue. Compromise won't bridge the gap.
You're just too different. There's no chance for balance, because you're on two ends of a very long seesaw. You just do things and see the world in two completely different ways, and ne'er the twain shall meet. That's when the trouble will start, because you won't be able to accept your differences; instead, you'll fight about them. You'll rely on your radical thinking to get you through an argument, but that will be no match for your pal's implacable stance.