There are variations on this theme that set them apart from the Old Apostolic Lutheran Church (first borns), or the older Church of the First Born (which also follows the Scandinavian Lutheran order of worship).
Related groups are Disciples of Christ, Christian Church (Independent) and Church of Christ (non-instrumental), as well as several Primitive Baptist associations (which are not African-American).
They strive to recreate the First Century Church and prohibit practices not mentioned in the New Testament ~ that includes the use of musical instruments.
The Disciples of Christ, the best known of the type, tried the First-Century idea but found problems so they shot for the Second-Century.
To a far greater degree than most of the members of these groups know their actual church practices are very much in line with traditional Eastern Orthodoxy (sans the hierarchy of bishops). Theologically they are not in dispute with the RCs except on questions of church structure and hierarchy. They should almost always come down in the same place with the Catholics when it comes to moral positions.
Peoples Temple originally began as a Disciples of Christ church, and was still affiliated with them when they went to Guyana. Of course, it was in name only, as Peoples Temple was in reality an early Liberation Theology/Socialist Theology “church”