An imaginative reading on the unity passage in John 17.
“That they may all be one, just as you, Father, are in me, and I in you, that they also may be in us, so that the world may believe that you have sent me.” (17.21)
First, the gospel of John was the latest among the four Gospels (ca. 80-90 AD). So, we shouldn’t be surprised if we found reference “for those who believe in me through their [the disciples’] word.” (17.20) By the time the gospel of John was written, John was the only apostle that still lived (and hence the story of John and Peter in John 21). So you would find a lot of Christians who never met Jesus in person; Christians who only managed to know him through the witness of the disciples. And hence Jesus prayed for the second and third generation Christians as well in the gospel of John. It established the relationship between Jesus with his followers no matter when they read the Gospel.
And during those early days of church growth, persecutions ran high and deep. As the world hated the disciples (17.14), the world will hate those who believe through the word of the disciples as well. That’s why Jesus was praying for unity, as unity would symbolize the power of the gospel. If the church is easily broken up (as evident by the disciples, as well, when Jesus was arrested; note that Jesus was praying for the unity of the twelve on 17.11), what will it imply about the god whom the church believe in? Certainly he is not worthy to be praised if his people’s allegiance easily crumbled under pressure. If they are united, perhaps then the world may believe that the Father has sent the Son (and hence the passage functioned as an encouragement as well for the church in those days).
The problem of church split is even more pointed, then, since usually it is due to internal cause. And hence it will be much worse than the break caused by persecution. Unity in the midst of persecution is much more than mere organizational unity. Unity is tested unity, through thick and thin of the church.
What if the church is more united in the time of adversity, e.g., like the Confessing Church in the time of Nazi? Well, I guess it would be a powerful witness of the Word (although, admittedly, the Confessing Church pitted themselves against the mainstream German churches, which they thought were full of errors by accommodating Hitler’s agenda into the church). The gospel is the power of God, indeed — and we are not ashamed of it (cf. Rm 1.16).