The axes are independent. You can have seamless friendships with people who are very different from you, and contentious relationships with folks who are just like you (but doing it wrong!)

There's nothing wrong with having to work at friendship. For years I had a friend that I looked up to (and, as it turned out looked up to me). We were both constantly striving to justify the other's faith and respect. It was a lot of work but incredibly valuable for both of us.