No, it did not. The permission of the Roman Pontiffs, formerly, to allow the TLM along side the NOM in the Roman Rite, was not the cause of disunity. We have an Eastern Rite in the Catholic Church and a Roman Rite (for the West) and that has not resulted in disunity. It is possible to have additional Rites or liturgies, and still have unity. There is a Anglican version of the liturgy, used by converts to Catholicism from Anglicanism. That was done for the sake of unity.
No, the TLM and the NOM are not to be blamed for the disunity. The blame is squarely on the shoulders of the conservative and traditionalist priests, theologians, and lay leaders, who promoted this disunity so as to have more power for themselves. Pride led them to constantly speak, before Francis was Pope, as if they each were the supreme judge of doctrine and discipline. A myriad of articles and videos were being circulated, in which each conservative or traditionalist with a following would represent his own views as definitive, and even subjugate the teachings of Popes or Councils to those views. Conservatives openly contradicted many different Church teachings, even dogmas of the Council of Trent, and their followers did not care. Neither did the editors of the Catholic media outlets care, if any of their popular authors taught a grave error.
Many times I wrote posts, before Francis, correcting conservative leaders, especially lay leaders, for grave errors in their articles. And few other persons noticed or cared. The authors in question did not care if their ideas were contrary to the Magisterium. The editors of Catholic publications did not care if the articles taught heresy. The leaders and the media outlets fed their viewers whatever they wanted, without regard for Christ and His Church.
Then when Francis became Pope, he was openly attacked by many different lay leaders and media outlets. For they had long prepared for this attack. They had long ago abandoned any concern for the Magisterium or the moral law. As long as a large audience wants malice and anger directed at the Pope, as long as they want all manner of absurd excuses for rejecting his teachings, that is what these lay leaders and “Catholic” media outlets will feed them.
The TLM is not to blame for this disunity. The lay leaders of the new evangelization, certain priests who developed a large following online, and the Catholic media outlets are to blame. They abandoned loyalty to the Magisterium long before Francis. God sent Francis to make their hidden errors manifest, and to offer them correction. And now every time they rail against the Pope, they show their own lack of Faith. And every time they lash out with malice against the Vicar of Christ, they show their own lack of Love. And that is the cause of this disunity — these lay leaders (and a few priests who imitate them) who have used their influence via the internet to exalt themselves above the Magisterium and gather a flock, each one gathering his own sheep into his own poorly constructed sheepfold.
And each of these lay leaders now has to attack the Pope, and has to argue against everything the Pope says and does, or he will lose his power over the sheep that he has stolen from the Lord. They are so much like the Pharisees of Jesus’ time, it is scary. It is one clear indication the End Times is near. The Pharisees have returned.
Why did the Pharisees reject Jesus? Some of them knew that Jesus was the Messiah (“this one is the heir”). They knew that Jesus of Nazareth was the long awaited Christ, the one who would be greater than Moses, greater than any prophet. They knew. And they had Him put to death anyway, so that they would not have to give up their positions of money and power, their positions of influence over the people, to become a mere follower of the Christ.
Similarly, some of these opponents of Francis know that the Church is indefectible, and that the teachings of Francis are not in grave error. But they have to fight against him, or they will lose their positions of influence over the many foolish lay persons who have decided to reject Francis. I don’t know how many of these opponents “know” this, but some at least. Others really think, in their pride and self-aggrandizement, that Francis is wrong. But their sins are not so much less than those who know.
I believe Francis is right to restrict the TLM, because of the foolish leaders who use the TLM to gather the weak in faith or the ignorant and draw them away from the Magisterium. But there’s nothing wrong with the TLM, it is simply not a suitable vehicle for salvation for most of the laity (nor for most of those we would like to convert). We could, in the near future, have both the TLM and the NOM.
We are just waiting for those who are adherents of the TLM to reject the heretics and schismatics among their leaders. We are waiting for these schismatics to walk away from the Church, take their fellow schismatics with them, and then we can be left in peace, and we will have both forms of the Mass.