How was the American reform movement influenced by religious beliefs?
The Second Great Awakening led to many reform movements in the 1830s and 1840s. The early abolition movement got its start here, as some in the North used the concept that all are equal in God's eyes in order to try to end slavery. There was also another pro-slavery movement in the South that used biblical references to slavery in order to condone it. Also during this period there was the beginning of the temperance movement. Temperance promoters used Proverbs 20:1, which is a verse that describes wine as "a mocker," in order to demonstrate that God does not want drunkards in His kingdom.
Later in the 1800s another religious revival led to reforms. The church was a very active social and reform organization in the US, and churchgoers would renew the push for temperance, ultimately ending with the Prohibition amendment and the Volstead Act in 1919. Women, who did not have much of a political outlet before 1920, were active in the church reform movements, and their work there would play a factor in the women's suffrage movement as well.
There have been many American reform movements that have been influenced by religious beliefs. Since you have tagged this with "1800s", I assume that you are talking about the reforms of the 1830s and 1840s.
The set of reforms that occurred in the 1830s and 1840s stemmed from (historians argue) the Second Great Awakening of religious fervor that was especially strong in the 1810s and 1820s. The Second Great Awakening is said to have encouraged people to believe that their society could and should be perfected. This led to such reform efforts as the push for abolition and the temperance movement.
The Second Great Awakening led to the idea that people could and should perfect themselves. This led quite naturally to the idea that they should also perfect their society. These ideas were instrumental in causing the reforms of the 1830s and 1840s.