The immediate cause of the Holocaust was racial hatred from a person who was definitely not even a Christian, and from those who supported him. Hitler did not profess to be Christian. His immediate circle of criminal gangsters were also not professed Christians. If anything, Hitler was a Pagan. He had great interest in the philosophy of Friedrich Nietzsche and in Norse Pagan religion.
But, having said that, it is extremely unfortunate to note that Christian groups in both Germany and Italy did not speak strongly enough at the time to renounce the despicable things done by the Nazis. For this reason, both the Lutheran and the Roman Catholic Churches bear some responsibility, not for causing the Holocaust, but for not preventing it. Christians ought to acknowledge this. Besides, there is a shameful history of antisemitism amongst professing Christians which can be traced all the way back to as early as the third century. Luther himself was embarrassingly antisemitic. So, Christians ought to acknowledge this shameful history and renounce it at every turn. But to say that Christianity caused the Holocaust is both untrue and is dangerous inflammatory rhetoric.
Having said that, I believe that Christians ought to spend more time acknowledging past sins in this area than calling out the lie and dangerous rhetoric of those who say this. Our first response ought to be with remorse and repentance rather than defensively calling out those who say these untrue things.
John Oakes