A zealot maybe? Some say literalists (because they interpret the word of the Bible literally I guess).
I have even found the title for these nineteenth-century religious Americans as "enthusiasts".
The fact that there are so many terms bandied about goes to show that there is no consensus.
At the time of the nineteenth-century, these men and women of God would probably have referred to themselves simply as Christians, or disciples of Christ.
Another term that crops up often to describe Christians of nineteenth-century America is "Evangelicals."
This movement was interesting because, it moved away from the Catholicism of Europe and developed Protestantism into Restoration Movement, the Latter Day Saint movement, Adventism, and the Holiness movement.
These movements in turn led to the "Third Great Awakening" which was a religious awakening that took place between 1850s to the 20th century.