What Was Good for Peter and Paul -
No, they didn't have the same approach. They were each forces of nature. Each had an extensive following. After disagreeing with each other from afar they had a meeting and decided to agree to agree on some points, agree to disagree on other points. Yet each could see the Christ in the other. Each could, in holy generosity, attempt to see things from the others point of view. And, in public, make peace.
Psalm 16:8 emphasises that our sights must be set forward - "I have set the Lord always before me; because he is at my right hand I shall not fall."
Peter and Paul could do it for God's sake and the sake of the Church ... it puzzles me why Katharine is willing and Rowan is not.
If it was good enough for Peter and Paul ...