They claimed to be.
The were certainly not good Christians and not representative of either modern Christianity as a whole or what modern Christians of any subset consider to be correct behavior for a Christian.
I think it would be reasonable to say they forfeited their claim to Christianity by their behavior, but it is not correct to say they did not lay claim to being Christian.
Not to argue with your points which are valid but my view is I really don't care what Hitler claimed to be. He was an unrepentent mass murderer. I usually make it a practice not to attempt to play God and wonder who is saved and who is not. But in Hitler's case there is not much of a question as his behavior was so extreme. Is there any record of Hitler and his inner circle going to church? Never heard of it. He did Satan's bidding and was most certainly not one of Christ's.