American reform movements have been influenced by such beliefs in at least two ways.
First, religion and philosophy have told Americans that they can and should make their society more perfect. This happened, for example, in the early 1800s when the Second Great Awakening helped bring the idea that society (just like people) could be perfected.
Second, religion and philosophy have served to support the specific goals of the movements. This can be seen in movements like the abolition movement, the temperance movement, and the Civil Rights Movement of the 1950s and '60s. In all of these cases, religion and philosophy have provided support for the goals that the movements were trying to achieve. They have helped to convince people that those goals were morally right.