I'm coming late to this thread ... till now I'd thought of "Bright Morning Stars" as an Appalachian carol, i.e. a ballad with a religious text closely related to the old folk hymns. It's not a shape-note song, since it doesn't appear in Christian Harmony, Sacred Harp, Harp of Columbia, etc., but its melody seems to come out of the same Anglo-Celtic oral tradition as some of the older shape-note repertory. After reading through all the posts, which strike me as being as authoritative as we're going to get unless somebody discovers new documentary evidence in the shape-note or Shaker traditions, I'd now classify it as a bluegrass gospel song that came out of southern Appalachian oral tradition.

Still, that's a pretty good pedigree!

Several posts questioned whether the text is Christian, but I think the imagery of the song is clearly grounded in scripture. Not only do we have the "bringt Morning Star" in Revelation, as several commenters noted, but to the time when "the morning stars sang together" in the book of Job. (Cf. the 16th-century Lutheran chorale "How Brightly Shines the Morning Star.") And the fathers, mothers, sisters, brothers imagery is common to a lot of American folk hymns.