Certain persons whose Christian faith compelled them to resist or act against the Nazi regime were definitely persecuted, amongst them the famous philosopher Dietrich Bonhoeffer. However, the phrasing of the statement implies that Christians were persecuted as a class, like Jews, gypsies, homosexuals, etc.. Aside from a few smaller non-mainstream sects, I am unaware of any wholesale persecution of Christians per se. Nazi ideology was none too sympathetic to Christianity, but they did not actively persecute the faith of the vast majority of the population.

It is also worth noting that they were obsessed with Catholic occult, collecting religious treasures and the like, but generally with the exception of Jehovah's Witnesses and some Catholic groups who tried to protect Jews, most Christians were not targeted. They are not atheistic, other then being non-religious as a political party. They do, additionally, form a cult of personality around Hitler; creating a political religion; linked to the Thule Society and mildly the philosophy of Jörg Lanz von Liebenfels.

The Nazis would not have explicitly claimed to be atheist, though this would be more for political reasons than religious ones - Communism, as propagated by Karl Marx and embraced by the Soviet Union, was explicitly atheistic, and Communism was an arch-enemy of the Fascist Nazi party. (Communism going hand-in-hand with atheism can also be seen to contribute to the boom of church membership in America during the 1950s). So the Nazis were not publicly atheist (any particular person's personal beliefs are largely unknown).

However, the Nazis can also not be said to be Christian by any reasonable metric of what defines Christianity. See the "German Christian" movement for more details on that, with the "Confessing Church" of Martin Niemoeller and Dietrich Bonhoeffer as the more authentically Christian counterpart. One interesting thing the German Christian movement did was follow in the footsteps of the early heretic Marcion in their efforts to "Aryanize" the German church.

So what were the Nazis? As /u/MyopiaPod noted below, they were not explicitly religious as a political party, but they did go to great lengths to create a political religion centered on the cult of personality around Adolf Hitler. You could reasonably say that Hitler was the god of the Nazi religion. It also incorporated a strong undercurrent of ancient paganism, especially Germanic paganism - the Nazis valued strength above morality, and sought to re-establish an authentic German nation free from all perceived "Jewish" influence. Historic Christianity was too "Jewish" to be allowed in the long run - it either had to be cleansed or supplanted. So if I had to characterize the spirituality of the Nazi party, one might say that the true Nazi god was the German nation and land itself, with Hitler as its great high priest, and a strong flavor of Germanic neo-paganism (source: Blainey, A Short History of Christianity, 2011).

Depends on what context you mean by "persecuted for their faith". There were certainly anti Christian tendencies within the Nazi Hierarchy, specifically towards Catholicism (due to its opposition to many of the Nazis eugenics policies as well as their hierarchy was seen as opposition to the Nazi ideal of having society completely submissive to the state) and Jehovah's Witnesses (due to their pacifism and refusal to submit to the authority of the state). But as a whole, Christians weren't openly seeked out and persecuted for their faith alone. The Nazi policy towards Christianity was complex and differed among person to person in the Nazi hierarchy. Hitler, Goebbels, Himmler, Heydrich, and Bormann were all opposed to Christianity, but given that German was largely Christian, it wouldn't be to their advantage if they had openly opposed it. So there was attempts to "Nazify" Protestant churches in Germany, in order to bring them over to Nazi ideology (while Catholicism was stealthily suppressed). While certain churches expressed pro Nazi attitudes, many of the resistance to the Nazis came from Catholics and Protestants. It is often believed by many that had the Nazis succeeded in their conquest, that they would have tried to rid Christianity of its influence in Europe, in favor of a more Nazi sympathetic form of Paganism. That being said however, there were committed Nazis whom considered themselves Christians, such as Bernhard Rust, Walter Buch, and Erich Koch. Certain early members of the Nazi party were also Christian such as Deitrich Eckart and Hans Schemm. But I would largely say that Nazism itself was largely anti-Christian at its core, seeing it as a temporary obstacle that they would have to manipulate if they were to succeed in their plans.