The Church of Judas was the Christian sect to which Arnold Rimmer's mother belonged.
Mrs Rimmer was a follower of this church, possibly before she joined the Seventh Day Advent Hoppists. The Church's beliefs were based on a myth that Jesus and Judas were identical twins. According to Arnold Rimmer, Judas's full name was James Judas Didimus, with both James and Didimus meaning Twin in different languages (this is inaccurate, as "Thomas" means twin in Ancient Greek, although "Didymus" was the Aramaic).
The Church believed that Judas took Jesus's place on the cross, so that Jesus could pretend to return after 3 days. Jesus then went to live in the south of France, married Mary Magdalene and invented the wheelbarrow.
Mrs Rimmer's reverence for the misunderstood Judas caused her to give her youngest son Arnold the middle name Judas.
Later, when Rimmer encountered identical twins named Jesus and Judas in 23 AD, he wanted to meet them but was stopped by his shipmates because of what had happened with Jesus of Caesarea. (RD: Lemons)