It depends on the denomination; one or two denominations of Christianity believe that once baptized you are a Christian forever, others do not.
That belief would contradict the Bible wouldn't it? There's the life of Judas Iscariot (who left the church as it were haha,) and there's this Bible Scripture:
John 6:66
(66)From this time many of his disciples turned back and no longer followed him.
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You might be right. But that line could be taken to simply mean those followers of Jesus only
physically stopped following him, it could be argued that they were still Christian.
Judas Escariot (btw, he was innocent) is condemned by the Church, but I don't recall him being directly condemned by Jesus.
REALLY?!?!?!
"23 Jesus replied, “The one who has dipped his hand into the bowl with me will betray me. 24 The Son of Man will go just as it is written about him. But woe to that man who betrays the Son of Man! It would be better for him if he had not been born.”
25 Then Judas, the one who would betray him, said, “Surely you don’t mean me, Rabbi?”
Jesus answered, “You have said so.” (Matt 26:23-25, NIV)
Bible Gateway passage: Matthew 26 - New International Version
"17 When evening came, Jesus arrived with the Twelve. 18 While they were reclining at the table eating, he said, “Truly I tell you, one of you will betray me—one who is eating with me.”
19 They were saddened, and one by one they said to him, “Surely you don’t mean me?”
20 “It is one of the Twelve,” he replied, “one who dips bread into the bowl with me. 21 The Son of Man will go just as it is written about him. But woe to that man who betrays the Son of Man! It would be better for him if he had not been born.”" (Mark 14: 17-20, NIV)
Bible Gateway passage: Mark 14 - New International Version
"21 But the hand of him who is going to betray me is with mine on the table. 22 The Son of Man will go as it has been decreed. But woe to that man who betrays him!” (Luke 22: 21-22, NIV)
Bible Gateway passage: Luke 22 - New International Version
I think perhaps you should read your Bible again.
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.