I have to agree with the previous post that John would certainly be classified as a Christian. Perhaps it depends on whether you define Christian as someone who follows Christ's teachings or someone who tries to follow them while admitting to human weakness.
Perhaps the most telling scene in terms of deciding whether or not John is a Christian would be the scene where he has to actually admit to his adultery publicly in order to try and bring the truth out in front of the court. This would provide a very compelling argument for those who try to follow the principles of Christianity as he sees his own weakness and tries desperately to right the wrong and is wiling to confront public shame to move towards what he thinks is right.
The play also shows a John Proctor who is conflicted about his faith. There is the issue with Reverend Parris and the money he spends on gold candlesticks. As the witch trials heat up, especially since he knows the truth, he loses faith in some of the church elders and the court, because they cannot see the farce for what it is.
I don't think Proctor ever abandons Christianity, per se, but without saying so, he may have abandoned Puritanism by the end. But then again, so did a lot of people at that time. By 1730, a mere 38 years after the Salem fiasco, there was no Puritan Church left in New England.
In the play "The Crucible" the Puritans were considered to be Christians. They lived a very strict and devout life that unfortunately was often judgmental of one another. John Proctor was also a human being and as everyone knows humans are susceptible to sin.
John made the mistake of cheating on his wife with Abigail who wants him to leave his wife. She makes up lies about Goody Proctor and causes her to be arrested for devil work. John went to her and pleaded with her, he lost his temper with her, but Abigail continues to hold firm to her accusations.
John redeems himself in the end when he refuses to comply with lying. He shows his true virtue by standing by the truth and dying for it.