How do schisms in the church fit into the plans of a monotheistic God?

I was reading this answer on the new Islam Stack Exchange, and it suddenly dawned on me that that schisms often fall along linguistic lines:

• The Great Schism divided Latin-speaking Christians from Greek-speaking Christians.
• The Protestant Reformation divided those who worshiped in Latin from those used the vernacular.
• Many of the approximately 38,000 Christian denominations have definite historical connections to particular languages. For instance, I grew up in a denomination that owes its existence to the desire of Swedish immigrants to worship in their first language.

Now there are a great many other reasons for these divisions; schisms have theological components as well. I'll address that aspect below. We read in Genesis that God is the source of language division:

And the LORD said, “Behold, they are one people, and they have all one language, and this is only the beginning of what they will do. And nothing that they propose to do will now be impossible for them. Come, let us go down and there confuse their language, so that they may not understand one another's speech.”—Genesis 11:6-7 (ESV)

So we have the story of a group of people trying to reach heaven by working together and God intervenes by confusing their language. Why is that? Why should God give humanity the power to make something great of themselves and then prevent them from doing it?

John Piper wrote in Desiring God (p. 44):

God loves to behold His glory reflected in His works. So the eternal happiness of the triune God spilled over in the work of creation and redemption. And since this original happiness was God’s delight in His own glory, therefore the happiness that He has in all His works of creation and redemption is nothing other than a delight in His own glory. This is why God has done all things, from creation to consummation, for the preservation and display of His glory. All His works are simply the spillover of His infinite exuberance for His own excellence.

As Piper explains in an appendix (p.310), the story of Babel is the story of God preventing humanity from making a name for itself to replace God's glory with our own. The church has, over two millenia, tried to reconstruct Babel. Left unchecked, there would have been no limit to what the church could have done. And so, God had to thwart our plans. The Holy Roman Empire was not allowed to permanently supplant the Secular Roman Empire, because, if it had, there would have been no room for God to display His glory via the Church.

But I think there's an even more compelling reason for church divisions in God's plan: the ministry of reconciliation. John's Revelation tells a reverse-Babel story:

After this I looked, and behold, a great multitude that no one could number, from every nation, from all tribes and peoples and languages, standing before the throne and before the Lamb, clothed in white robes, with palm branches in their hands, and crying out with a loud voice, “Salvation belongs to our God who sits on the throne, and to the Lamb!” And all the angels were standing around the throne and around the elders and the four living creatures, and they fell on their faces before the throne and worshiped God, saying, “Amen! Blessing and glory and wisdom and thanksgiving and honor and power and might be to our God forever and ever! Amen.”—Revelation 7:9-12 (ESV)

Voices from every language will, before this age is over, join in one voice to glorify God. Jesus will accomplish this and has accomplished it through His extraordinary sacrifice. You don't have to look very far to see that such a reconciliation could only be accomplished by the sovereign will of God. Whatever mighty works humanity can do, it can't unite itself by itself. Only God can claim credit.

So why are there theological differences? I'd like to suggest they exist because no one person or organization can really grasp the depth and breadth of God's glory. One of my friends got excited about Hesychasm a while back and told me about the incredible Christians who live on Mount Athos. That anyone could spend all of their waking moments in continual prayer seems simultaneously inspiring and tragic. On the one hand, they are missing out on so much of what God is doing, and on the other, I am missing out on so much of what God could be doing through me. It's remarkable to me that God simultaneously encourages His people to explore the full range of His creation while encouraging other to mine in one place for His richness buried under the surface.

As a Protestant, I find that I can agree with almost everything that my Orthodox and Catholic brothers and sisters proclaim about God. Generally, the problems come with a few edge cases and with emphasis. In that main, we are in agreement. Further, our differences will sort themselves out when Jesus returns to take us as His bride.

Short Answer: Reformation and such prepares the ground for religious freedom and an actual restoration of the one church of Jesus Christ.

If you dismiss the claim that up until the first big shism in 1054 (according to you), that there was one "universal, apostolic" church, you get a wholly different picture. The only way a reformation can make sense is that the reformators saw or believed to see, that the church had gone the wrong way. So, as much as they could, and with their understanding, they tried to correct what had gone wrong and voilà, you end up with thousands of different understandings of what is right, that you have today.

See, the point is, except for catholics, this only makes sense if the church really did go astray. And then men come and think they can fix it? Well, they did what they could, didn't they?

Anyway, what this did achieve is that, after many years of struggle and religious conflicts, we have religious freedom (in most parts of the world). This set the stage for an actual restoration of the church of Jesus Christ (albeit still with much persecution) in the 19th century, complete with divine authority and everything.

Now would be a good time to speak to local LDS missionaries ;-)

Even if you don't buy the restoration part, we have come to a situation where, for the first time in history, individuals have a choice of what to believe. Surely that should make their belief, so they choose to believe, deeper?

The traditions of the church and all the different denominations in the world have nothing to do with true Christianity except where they help individuals to follow Christ.

The Church in it's many forms are but organizations made by men, not Holy, but flawed institutions with flawed rules and regulations.

Yet God uses these institutions to spread the Truth. But it is the individual alone who meets God "in the dark night".

Matthew 15:8 “‘These people honor me with their lips, but their hearts are far from me. 9 They worship me in vain; their teachings are merely human rules.’”

and

Luke 9:49 “Master,” said John, “we saw someone driving out demons in your name and we tried to stop him, because he is not one of us.”

50 “Do not stop him,” Jesus said, “for whoever is not against you is for you.”

and

Matthew 7:21 “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but only the one who does the will of my Father who is in heaven. 22 Many will say to me on that day, ‘Lord, Lord, did we not prophesy in your name and in your name drive out demons and in your name perform many miracles?’ 23 Then I will tell them plainly, ‘I never knew you. Away from me, you evildoers!’

The times of disagreement and division within the worldwide church have also been some of the times when we have benefited from deeply progressing in our understandings of God and the Bible.

• The early church was forced to think deeply about the nature of the Trinity when confronted by those with different beliefs, leading to the production of the early creeds
• The protestant reformation prompted both the reformers and the Roman Catholic Church to reform and clarify their understanding of salvation
• Puritans and other later protestants split from their countries' establish churches, which has led to better understandings of ecclesiology
• The on-going split in the Anglican communion is leading many people to thinking deeply about our doctrines of the inspiration and authority of scripture
• The current debate between cessationism and continuationism is leading to deeper understandings of the work of the Spirit in the lives of Christians

The pressure of division is helpful when it makes Christians think deeply and reform their beliefs. This can be seen most clearly with the earliest debates over the nature of the Trinity: as far as I know those early non-Trinitarian churches all died off, and Christians since then have been united in their understanding of the Trinity. (Though newer non-Trinitarian churches have arisen since then, but they are not descended from those early ones.)

C.S. Lewis actually made an argument in favor of the division of the church - namely, that an institution with a single earthly head could be far more easily swayed by the Devil. By fragmenting the church, Christ has protected it from the deceit of the Evil One.

Additionally, as Paul says in 1 Corinthians 12:

12 Just as a body, though one, has many parts, but all its many parts form one body, so it is with Christ. 13 For we were all baptized by[c] one Spirit so as to form one body—whether Jews or Gentiles, slave or free —and we were all given the one Spirit to drink. 14 Even so the body is not made up of one part but of many.

It is my personal observation that different denominations do different jobs in the "church" as a whole. Some denominations are better at social gospel ministry, others are more scholarly, and yet others are better at encouraging worship. By having different part sof the body develop particular strengths, the body as a whole can learn from itself.

Finally, it should be remembered that even Paul understood that the point of preaching was to "become all things to all men", for as he says:

19 Though I am free and belong to no one, I have made myself a slave to everyone, to win as many as possible. 20 To the Jews I became like a Jew, to win the Jews. To those under the law I became like one under the law (though I myself am not under the law), so as to win those under the law. 21 To those not having the law I became like one not having the law (though I am not free from God’s law but am under Christ’s law), so as to win those not having the law. 22 To the weak I became weak, to win the weak. I have become all things to all people so that by all possible means I might save some. 23 I do all this for the sake of the gospel, that I may share in its blessings

And if Christ is preached out of impure motives, that doesn't matter either. As Phillipians says:

15 It is true that some preach Christ out of envy and rivalry, but others out of goodwill. 16 The latter do so out of love, knowing that I am put here for the defense of the gospel. 17 The former preach Christ out of selfish ambition, not sincerely, supposing that they can stir up trouble for me while I am in chains. 18 But what does it matter? The important thing is that in every way, whether from false motives or true, Christ is preached. And because of this I rejoice.

Does this mean that the fragmentation of the church is actively good? No. But even still, even in its broken state, God can use it to accomplish things He desires.

In Orthodoxy, G. K Chesterton argues that Christianity consistently strives to balance two sorts of opposite extremes. He mentions, for instance, that our religion has been criticized for being far too weak and submissive while being equally faulted for promoting wars and anger. The paradox extends all the way back to Jesus himself: he was a lion when he cursed the fig tree, rebuked Peter, and turned over the money-changers' tables and a lamb when he taught non-violence, washed his disciple's feet, and allowed himself to die an innocent man. Chesterton argued that the balance was not maintained in the church by drawing inward to a central (safe) compromise, but rather by exaggerating opposite extremes:

The Church could not afford to swerve a hair's breadth on some things if she was to continue her great and daring experiment of the irregular equilibrium. Once let one idea become less powerful and some other idea would become too powerful. It was no flock of sheep the Christian shepherd was leading, but a herd of bulls and tigers, of terrible ideals and devouring doctrines, each one of them strong enough to turn to a false religion and lay waste the world. Remember that the Church went in specifically for dangerous ideas; she was a lion tamer. The idea of birth through a Holy Spirit, of the death of a divine being, of the forgiveness of sins, or the fulfilment of prophecies, are ideas which, any one can see, need but a touch to turn them into something blasphemous or ferocious. The smallest link was let drop by the artificers of the Mediterranean, and the lion of ancestral pessimism burst his chain in the forgotten forests of the north. Of these theological equalisations I have to speak afterwards. Here it is enough to notice that if some small mistake were made in doctrine, huge blunders might be made in human happiness.—Chapter 6, "The Paradoxes of Christianity"

Now Chesterton was not arguing for schisms. He, in fact, points to a tradition that I find very compelling as one of the dangers the Church avoided:

It would have been easy, in the Calvinistic seventeenth century, to fall into the bottomless pit of predestination. It is easy to be a madman: it is easy to be a heretic. It is always easy to let the age have its head; the difficult thing is to keep one's own. It is always easy to be a modernist; as it is easy to be a snob.—Chapter 6

But it seems to me that the very same arguments about avoiding the dangers of destructive doctrine also apply to the Church's avoidance of destructive hierarchies. Oddly enough, I arrived at that conclusion when reading elsewhere in Orthodoxy:

If any one wants a modern proof of all this, let him consider the curious fact that, under Christianity, Europe (while remaining a unity) has broken up into individual nations. Patriotism is a perfect example of this deliberate balancing of one emphasis against another emphasis. The instinct of the Pagan empire would have said, "You shall all be Roman citizens, and grow alike; let the German grow less slow and reverent; the Frenchmen less experimental and swift." But the instinct of Christian Europe says, "Let the German remain slow and reverent, that the Frenchman may the more safely be swift and experimental. We will make an equipoise out of these excesses. The absurdity called Germany shall correct the insanity called France."—Chapter 6

We would be hard-pressed to consider Europe as the center of Christendom these days, but the principle of one portion of the whole balancing the opposite tendencies of another portion seemed to be at work in the Church Universal. In essence, we correct the problem of one branch being weighed down be ritual with another branch that is perhaps too unfettered by it. We balance the insufficiently grounded faith with another that is deeply rooted. Rather than turning the tree into a stable stump, we allow both roots and branches to flourish equally.

If it were God's will we (Catholics) probably wouldn't pray for reunification every Good Friday!

For Unity of Christians:
Let us pray
For all our brothers and sisters
Who share our faith in Jesus Christ,
That God may gather and keep together in one church
All those who seek the truth with sincerity.

Almighty and eternal God,
You keep together those you have united.
Look kindly on all who follow Jesus your Son.
We are all consecrated to you by our common baptism.
Make us one in the fullness of faith,
And keep us one in the fellowship of love.
We ask this through Christ our Lord.
Amen.

on the other hand

At the Easter Vigil Mass a few days later when we thank God for the "Happy fault of Adam" that did more damage to humanity than any schism is capable.

So, maybe in a few hundred years we'll all be thanking God for the "Happy fault of Luther", who knows?

It's clear enough, since so much hatred and bitterness were caused by schisms, that it is not the active will of God for His Church. But it is something God allows us to work out for ourselves, through His passive will. Probably to be tested and purified (ala Zech 13:9).

Specifically to the point of schism, canon law says

Can. 751 Heresy is the obstinate denial or obstinate doubt after the reception of baptism of some truth which is to be believed by divine and Catholic faith; apostasy is the total repudiation of the Christian faith; schism is the refusal of submission to the Supreme Pontiff or of communion with the members of the Church subject to him.

Modern day Protestants, practicing their traditions, are neither heretics nor schismatics.

See also, CCC 817-822

I basically agree with last two of Jon's answers (here and here), but I'd like to add some Catholic perspective to it. As Jon interpreted Chesterton, there have always been different groups in the Church, approaching on extreme or the other. Rivalities between monastic orders within Catholic Church show this quite well: opposition between Franciscans and Dominicans and later between both Franciscans and Dominicans on one side and Jesuits on the other is well known (many Catholic jokes are about this), but all stayed in the "club" mode and in unity with whole Catholic Church, enriching its tradition with their intellectual and spiritual contests. This is easy in Holy Spirit and in love, but hard when sin plays the main role. That's why many groups went "clique" and left the Catholic Church.

Even more different, and in positive way, are parts of Catholic Church that re-entered full communion after some time away from the visible Catholic Church. It's really enriching to participate in Divine Liturgy of John Chrysostom and still know that it is completely the same Church and one faith (not just "one faith, but..."), just different tradition of expressing the one faith. It is highly unlikely that these traditions would have evolved to this richness if full unity would have been maintained from the beginning. I believe these are the first fruits of the full re-unification and countering the "Babel effect" as described in the Revelation.

For Protestants, this unity in difference is not so clear, because Protestant oecumena treat different denomination in a similar manner as different orders and congregations are treated in Catholic church.