Jürgen Moltmann said that the Anabaptists "were the only Reformation movement by faith alone" because "the Anabaptists rejected the foundations of the Christian state religion." Moltmann argues that Constantine had united the Church with the Holy Roman Empire, and salvation was mediated through it. The Anabaptists were the only ones to reject this imperial state religion, because all the other reformers aimed to reform the Christian state religion without abolishing it. The Anabaptists rejected infant baptism, because it stood for membership into the Christian state (apart from faith), and they rejected oath taking and violence, which were indispensable to the Christian state, and they rejected Christian government, because government was not a Christian task. The Anabaptists believed in salvation by faith alone, apart from all Christian states, and for this reason they were hated by all other Protestants and Catholics alike who serve the religious state cult to this day, and many of them, including Michael Sattler and Dirk Willems were executed by the Christian states as heretics for rejecting imperial state religion.
Jürgen Moltmann spoke at the "Unfinished Worlds: Moltmann at 90" Conference in 2016 at Emory, at which I attended and transcribed his following comments regarding the Anabaptists (c.f. Emory's video of Moltmann's lecture):
Who were the Anabaptists? And why were they persecuted so cruelly by Catholics and Protestants in common. Martin Luther called them "fanatics". Historians speak of the "left wing of the Reformation". I think they were the only Reformation movement by faith alone! After Reformed biblical sermons were preached, and the people has consented, the magistrate of a town, or the prince of the country, carried out the reformation of churches and schools. The Reformation took place within the laws and institutes of the corpus christianum, that is the Holy Roman Empire of the German Nation. Constantine and Byzantine Caesars, who followed him, made Christianity into their imperial state religion, and their empire into the kingdom of Christ, the millennium of Christ.
The Reformers remained true to the possibilities of this corpus christianum, but the Anabaptists rejected the foundations of the Christian state religion—they replaced infant baptism, by which every child becomes automatically a christian citizen, by believer's baptism. They refused the service of the sword—Jesus forbids the violence of the sword. They rejected givings and oaths—Jesus forbids his followers from taking an oath. They took no part in government, because it is not a Christian government, because it is not a Christian task to be government—these references to Jesus and his sermon the mount, are to be found in the Anabaptist Schleitheim Confession (1527), written by Michael Sattler. What the Anabaptists did politically was to reject the idea of a Christian empire, and the Christian state religion, therefore they were persecuted, on the grounds of imperial law. They were enemies of the Holy Empire, and heretics of the State religion. 
After Moltmann's initial argument (see quote above), he tells the story of the Anabaptist founder, Michael Sattler, who wrote the Schleitheim Confession (1527), and was put to death as a heretic for his faith (and rejection of the Christian state religion). His comments explain the Christian devotion of the Anabaptists, and also explain their opposition from other Protestant defenders of imperial state religion.
During the Inquisition in Rothenburg, Michael Sattler, who wrote the Schleitheim [Confession], said when the Turks are coming, do not resist, because it is written, 'you shalt not kill'. And thus, the danger presented by the peaceful Anabaptists, became practice. The Anabaptists were a threat to the survival of the Christian empire. And they had incurred resentment among the people. Michael Sattler's execution in 1527 in Rothenburg, next to Tübingen, was most cruel. They cut his tongue out of his mouth, and they chained him on a wagon, and burned him outside of the town. His wife, Margaretha, refused any attempt of rescue, and they drowned her in the Neckar river.
Michael Sattler was a prior of the well known monastery St. Peter in the black forest. He was a theologian and a humanist. In 1525, he was a rebellious [peasant in the Peasant's Revolt], in the same year he joined the Anabaptists in Zurich, and preached in the villages around Tübingen and Rottenberg, and baptized many in the Neckar river. His message was "Christians are completely calm, they trust their father in heaven, they live without worldly armament." Like Michael Sattler, Anabaptists in the Reformation time, are ready for martyrdom. One of their hymns begins, 'how lovely is the deaths of the saints'. 
In the header to this blog, I've included a famous depiction of the Mennonite martyr Dirk Willems, who was fleeing from a "thief-catcher", after being condemned to death for his Anabaptist beliefs. As Dirk Willems fled, the thief-catcher in pursuit fell through thin ice. Dirk Willems had compassion on the thief-catcher, turned around and saved the thief-catcher from drowning. Dirk Willems was repaid by being apprehended and then burned to death by a "lingering fire". Dirk Willems embodies how the peaceful Anabaptists have been treated with violence since the Reformation, by Catholics and Protestants, and these injustices must be made right.
Damnation and Persecution of the Anabaptists today.
Moltmann raised this concern: The Augsburg Confession (1530) condemns the Anabaptists to this day, and the Book of Concord has no explanation for these statements, Moltmann said "how can a Lutheran candidate be ordained on the Augsburg Confession today?" Moltmann praised the Lutheran World Federation for asking the African Mennonites for forgiveness in recent years, but Moltmann believes that this gesture cannot be made without consequences. Moltmann proposes in the following quote that such a gesture must be accompanied by either a revision of the Augsburg Confession or amendment to the Book of Concord, and I believe this is worth repeating loudly:
In view of the Anabaptists, I'd like to make . . . remarks. A few years ago, the Lutheran World Federation, asked African Mennonites forgiveness for the damnation and persecution of peaceful anabaptists, during the Reformation time. In my opinion, this gesture must have consequences. Namely, the revision of the Augsburg Confession (1530) or a commentary in the Book of Concord, stating that Lutherans today no longer condemn Mennonite's peace making. Otherwise, how can a Lutheran candidate be ordained on the Augsburg Confession today? Action must follow gestures. We no longer condemn Mennonites, and the Church of the Brethren as fanatics, . . . but appreciate them as historical peace churches. 
Here are some of the condemnations of the Anabaptists currently in the Augsburg Confession (1530):
Article V.4: "They condemn the Anabaptists and others who think that the Holy Ghost comes to men without the external Word, through their own preparations and works."
Article IX.3: "They condemn the Anabaptists, who reject the baptism of children, and say that children are saved without Baptism."
Article XII.7-8: "They condemn the Anabaptists, who deny that those once justified can lose the Holy Ghost. Also those who contend that some may attain to such perfection in this life that they cannot sin."
Article XVI.3: "They condemn the Anabaptists who forbid these civil offices to Christians."
Article XVII.4: "They condemn the Anabaptists, who think that there will be an end to the punishments of condemned men and devils." 
The Anabaptist tradition originated in the Radical Reformation, and is represented today by the Amish, Mennonite, Church of the Brethren, and many other churches today. (The Anabaptist are not the same as Baptists—both groups reject infant baptism, but for different reasons and they are different church traditions.) During the Reformation, the Protestants and Catholics disagreed on everything, but were united in their mutual hatred for the Anabaptists. It's a joke we laugh at, that is no laughing matter, because many Anabaptist Christians were put to death for their beliefs (via capital punishment) by Protestants and Catholic Christians. On the 500th anniversary of the Reformation, I believe there is no better time to seek reconciliation with Anabaptists than right now. Forgiveness is a first step, but not a gesture without consequences, so let us seek reconciliation.
1. Jürgen Moltmann, Future Worlds: Moltmann at 90. transcribed by Wyatt Houtz. [ See Emory's video recording of this lecture here: https://vimeo.com/189203093#t=43m15s ]
3. Moltmann. Ibid.
5. Augsburg Confession (1530) [Bold added for emphasis].
Related: anabaptists, Emory, Jürgen Moltmann, Mennonites, Unfinished Worlds: Jürgen Moltmann at 90