This is a very insightful question. Sometimes the differences in interpretation of Scripture and Tradition seem overwhelming. However, unity is possible because Christ prayed for it at the Last Supper “that they all be one…so that the world may believe.” Thus, as John Paul II said in Paragraph 20 of Ut Unum Sint, “the movement promoting Christian unity, is not just some sort of “appendix” which is added to the Church’s traditional activity. Rather, ecumenism is an organic part of her life and work, and consequently must pervade all that she is and does.” (See: http://www.vatican.va/edocs/ENG0221/_INDEX.HTM)
So unity is possible, it’s just a matter of how. The principle to keep in mind here is that of convergence (which is very different from compromise ). Namely, in the theological dialogues, delegates begin first by exploring what their traditions already agree upon. Then they move on to those issues which are still divisive. Almost always, we find that what we have in common is much more that what still divides. As they continue their deliberations, sometimes for years or even decades, new insights and articulations emerge in which both sides can recognize the full expression of their faith. This is the point of convergence. It takes time, lots of effort, and LOTS of grace. But the Holy Spirit, the Spirit of Unity, is very much at work in the process.