Can There Be Christian Unity Without Doctrinal Unity?

I recently finished reading a book called "Your Church is too Small" (Why Unity in Christ's Mission is Vital to the Future of the Church). The writer was seeking to unite Catholic, Protestant, and Orthodox Christians.

His message to Protestants was to respect the ancient creeds, and to know something of early Church history. His message to the Catholics and the Orthodox was to ease up on strict doctrinal adherence as a prerequisite for unity. Although the author believed that there are certain doctrines that we should all hold in common, he also believed that there are some upon which we should agree to disagree. In other words, some doctrine is important and some is not. He believed that our unity should be based, not upon doctrine, but upon our shared mission to evangelize the world.

Although there was much of value in the book, the author never stated which doctrines he felt were important and which were not. Neither did he say who within the Christian world would make such a decision, or why he felt there would be unity around such a decision.

The most important thing that he left out was any sort of Biblical support for the idea that some doctrines are important and others are not. Much of Protestant "unity" is based upon this concept, but I have yet to find any Biblical support for it. In fact, a quick word search for "doctrine" reveals that adherence to the Apostle's doctrine is considered to be of utmost importance by the Biblical writers.

So the question is, can God really bring unity around a concept that is not Biblical?