So was Judas still a Christian after he betrayed Jesus?
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No but the reason why is not because of the betrayal but because of the time line and definitions. By definition a Christian is someone who believes a certain set of things, but one of them is a belief in the resurrection of Jesus. This was established at the First Council of Nicea and by that definition it means that, according to scripture, the first "Christian" was Mary Magdalene because although the gospels differ regarding who was present when Jesus' tomb was found empty, Mary was always among them. Thus, Magdalene's real significance is not all that Da Vinci Code bullshit, for which there is no evidence at all, but that it was her who may have been the first believer in the resurrection and thus the first "Christian" as we define it.
Since scripture tells us that Judas either hanged himself or fell off a cliff prior to the resurrection or Jesus revealing Himself, then Judas could not be a Christian because he was dead before belief in the resurrection began to take root. Thus Judas could not have "remained a Christian" because Christianity did not exist until he was dead. So he never was one to begin with.
Beyond that, you have to keep in mind that the apostles did not believe they were starting a new religion. They believed they were guiding Judaism into the next (and final phase) according to the Messianic prophecies. This is spelled out quite clearly in the genealogy outlined in Matthew 1 wherein every 14 generations something significant happens that represents a radical change in the course of Judaism.
It is written in Luke 17: 4
"Even if they sin against you seven times in a day and seven times come back to you saying 'I repent,' you must forgive them." Thus we can argue that had Judas repented and asked forgiveness he would have been forgiven, but he died (either by accident or by his own hand) prior to that and so.....well...tough titty for him.