Christianity is the religion of those who follow Jesus Christ. Atheism is the religion of those who don't believe there is a god. Jesus Christ, in the Bible, said himself that he was God's son, born of the virgin Mary. If you do not believe what Jesus says is true, how can you follow Him? Without God, there is no Jesus. Christianity and Atheism are in direct conflict with each other - one says there is a God, the other says there isn't. Therefore, you cannot say that you believe in and follow Jesus Christ if you do not believe in God.
I consider myself a Christian Agnostic which is a Agnostic theist who believes in the views of Christianity. You have to believe in a God of the Bible who is Yahweh be a Christian. Atheism and Christianity are complete opposites. They can't be mixed together no matter how hard you try.
My son posed this argument to me the other day, saying one that follows the teachings of Jesus is a Christian just as long as they follow Jesus' 2nd commandment. One important missed tenet of Jesus' teachings is the 1st of His 2 commandments, which is to love Gove with ones whole heart, soul, & mind. So, following the Golden rule, as many non Christians do, does not lend itself to be able to call oneself a Christian. Just a nice person, but certainly not a follower of Jesus, which precludes them from Christianity by default.
Atheists are not Christians if they do not believe in God. God is the center of Christianity and Christians are followers of Christ. There is no way that an Atheist can be considered a Christian if do not believe in God. The concept is ludicrous and should not even be up for debate.
Atheists are typically people who do not believe in any religion nor any God. Since God plays a major role in Christianity, I don't think there could be a true atheist who is a Christian and vice versa. Jesus Christe is believed to be the son of God, so as per authentic Christian faith, one must believe in God if they believe in, follow and serve his son, Jesus Christe.
Christian Atheism should be seen as a form of atheism or humanism with distinctively Christian characteristics rather than a branch of Christianity with atheistic characteristics. It cannot be considered properly Christian as the central tenant of Christianity is faith in the existence of a transcendental God with the characteristics of classical theism - omnipotence, omnibenevolance and omniscience.