From the ecumenical movement to the weirdest of cults, all religious organizations strive for unity. While mainstream denominations have all but given up on unity with each other, they still struggle for internal unity.
Unity is essential to God's plan. Jesus prayed for it (Jn. 17:23), and the Holy Spirit inspired the apostles to make it one of their central themes (1 Cor. 1:10, Eph. 4:1-16, Phil. 1:27). To discard it as impossible shows a lack of faith in the power of God (Rom. 1:16).
There are only two ways that unity can be attained within a religious organization: (1) the members conform themselves to God's will, or (2) they conform themselves to the directives of some human leadership.
When a religious organization gives up on the first route toward unity, it defaults to the second. Evidence of this includes the presence of man-made councils, conferences and other organizations, the loss of local church autonomy, and the voting on articles of doctrine.
God's way requires that every member of His church acquire the knowledge and understanding of His word so that they do not have to depend upon men to attain unity. Hebrews 8:7-13 shows that this was God's will when he designed the New Testament in all of its simplicity.
Considerable individual effort is required to attain God's will of unity. This unity is quite delicate, since any member can cause disruption through ignorance or contention. This places a tremendous responsibility upon every member of the Lord's church.
On the other hand, individual obedience is effective in producing unity. It works. We can observe the consistency of churches throughout the world that have nothing else in common except faith in God's word as their sole source of authority. No conferences. No conventions. No super-leaders. No organizations. No creeds. Nothing but the bible.
The sign "Church of Christ" is not the source of this unity. Many who use this designation have departed from the sound doctrine. This should not be surprising; it was prophesied in Mt. 7:15-23, 2 Tim. 4:3-4, 2 Pet. 2, Jude 3-4, and many other places.
Unless they return to the truth, they will soon set up a governing body of men superior to the local eldership to maintain unity within their ranks. Many have already done so with sponsoring churches, societies, and other arrangements to attempt to enforce unity. This is the inevitable result of digression, and it also provides ample evidence that the organization is no longer operating under God's established authority.