Was Hitler Catholic?

No introduction necessary

There is a rumour going around that Hitler was Catholic. But then, there is a rumour going around that he was Jewish, and another that the Holocaust never really happened.

It is true that Hitler was baptized and confirmed as a Catholic. His mother, after all, was Catholic, though his father seems to have been atheist.

His later public statements can also be quoted to imply some sort of theistic faith.

But there is, in the end, conclusive proof that he was not Catholic:

1. As an adult, he never attended mass or took the sacraments. That would have meant automatic self-excommunication after one year. 
2. In the early 1830's, the German bishops excommunicated everyone who joined the Nazi Party, or even flew the Nazi flag. At this time, Hitler was the leader of the Nazi Party. Accordingly, he was publicly excommunicated. He made no effort after this to reconcile with the church. 
3. The official doctrine of the Nazi Party was paganism. This was by Hitler's choice: he appointed Alfred Rosenberg as official party ideologue, and Rosenberg was a vocal anti-Catholic. 
4. Hitler's plans for a postwar new German capital allowed no churches. 
5. Hitler actively persecuted the church when in power. Wikipedia gives chapter and verse. 
6. While his public statements are unclear—he speaks often of “divine providence”--Hitler's private conversation seems to have been resolutely anti-Catholic. Many of his actual comments are preserved in Hitler's Table Talk. Speer, Shirer, Goering, Goebbels all understood him to be anti-Catholic. Hitler was a politician, and a completely unscrupulous one. His public statements were calculated for political advantage. His private talk reveals his true views. 
7. Hitler killed himself, without taking last rites, and had his body burned. All three acts were against church teaching and would, in the mind of a believing Catholic, have guaranteed him a warm reception in Hell. It follows that he cannot have been a Catholic at the time of his death.