I don't think Oriana Falachi is trying to be anti-Christian just for the sake of it. She's from a heavily Catholic country, and isn't saying "Christian" to mean "Protestant", but rather anyone believing in Christ, any Christian faith. And, while I heartily agree that Hitler and his henchmen weren't in any sense Christian, they came from a Christian country/background/part of the world.
Do not forget this famous quote:
First They Came for the Jews
First they came for the Jews
and I did not speak out
because I was not a Jew.
Then they came for the Communists
and I did not speak out
because I was not a Communist.
Then they came for the trade unionists
and I did not speak out
because I was not a trade unionist.
Then they came for me
and there was no one left
to speak out for me.
Pastor Martin Niemöller
So I think it is in this sense that Oriana lays some of the blame for the Holocaust on European Christiandom, for not standing up and stopping the monster Hitler and his friends.