"Let the Church Roll On" is in two collections of spirituals; age uncertain, possibly late 19th c.:
E. A. McIlhenny, "Befo' de War Spirituals, Words and Melodies," 1933.
Grissom, M. A., Negro Sings a New Heaven. Univ. North Carolina Press, 1930. Grissom calls it a favorite shout song.
It is well-known among whites in the southeast, and has spread to the Caribbean. Flatt and Scruggs, Stanley Brothers and Doc Watson have recorded it, and the Smithsonian recorded The Missionary Quartet singing it in the Bahamas.