The unity Christ prays for in John 17 has its focus on the glory of God and is produced by the love of God. So if this unity is truly focused on God’s glory, then all self-focus is banished. It’s true that along with abandoning Christ’s teaching, the other major way that disunity can occur is seeking one’s own glory. Jesus stated this clearly in John 7:18 He who speaks from himself seeks his own glory; but He who is seeking the glory of the One who sent Him, He is true, and there is no unrighteousness in Him.
The glory of God is that which is most valuable or significant in all of creation and it has been given to all who believe. This will be a predominate characteristic in the church and that which unbelievers are unable to pursue. That’s because unbelievers destructively exchange God’s glory for the glory of created things. However, when someone believes in Christ, that person is rescued from that way of life and is enabled to live for God’s glory instead. That rescue is God’s love and so those who understand God’s love in that way will be eager to give God glory for that gracious work in their lives.
This includes conversion—1 Pet. 2:9 But you are a chosen race, a royal priesthood, a holy nation, a people for God’s own possession, so that you may proclaim the excellencies of Him who has called you out of darkness into His marvelous light… And also sanctification—Heb. 13:15 Through Him then, let us continually offer up a sacrifice of praise to God, that is, the fruit of lips that give thanks to His name… And lastly, whatever ministry takes place—2 Cor. 4:15 For all things are for your sakes, so that the grace which is spreading to more and more people may cause the giving of thanks to abound to the glory of God.
The point is that when Christians truly imbibe these beliefs, everyone testifies that to be saved by grace, to be growing by grace and to minister to others by grace is all to the glory of God. Thus when Christians have these mindsets, they share in the unity of the Triune God and testify to the work of Christ, who was sent by God to bring about this result of fully unifying God’s people in his redemption of love.