Pastor Tribulation Wholesome, the pastor of Amsterdam, and his sidekick, Ananias (named after, as Subtle says, "the varlet who cozened the apostles"), a deacon, likely were quite recognizable to Jonson’s audience and public as Anabaptists. The Anabaptists are sometimes called the Brethren in the play (see Act 2, Scene 5). Anabaptists belonged to a religious movement founded by Muentzer (pictured) and known as Wiedertäufer in Germany. Such Christians, in the extreme form that Jonson satirizes, have since disappeared, but their religious tradition lives on.
The Amish religion is a possible modern analogue for elements of Anabaptism. Anabaptists, like some other Christian denominations today, believed in adult baptism, and they thus dissented from mainstream Christianity. The principle here was that baptism was for believers who had repented of their sins—while small children and babies were unable to do so. The alternative, paedobaptism, child or infant baptism, relied on the faith of the parents or, at least, the Christian community, to bring the child into the Church. This was no small disagreement—the first president of Harvard University, Henry Dunster, was fired from that position in the mid-1600s because he had refused to baptize his children. This issue of theology and church practice remains contested today.
An in-depth understanding of Anabaptist practice is not essential to understand The Alchemist, but it is worth realizing that the Anabaptist movement was a serious, fervent movement in Protestantism, driven by equality and asceticism, perhaps a more extreme form of other similar movements. John of Leyden, a contemporary Anabaptist, declared that "all things were to be in common, there was to be no private property and nobody was to do any more work, but simply trust in God."
What Jonson satirizes in the Anabaptist characters, above the overzealousness of Ananias (already a satire: Ananias in the New Testament held back some of his money from the nascent Church), is the contradiction implied in the Church militant, that is, a religion of peace being used for military conquest as a means of spiritual conquest.