Hitler put Christian belief into practice.
In his writings, Martin Luther - the founder of the second-largest branch of Christianity - laid out his vision for how a Christian society should operate. Hitler was inspired by these writings and followed them.
Hitler used Luther's religious writings as almost an instruction manual. Luther's writings were handed out at Hitler's rallies. I don't see how this can't reflect back on Protestantism at the very least.
Naziism in general and Hitler's personal philosophy drew heavily from fundamentally Christian sources. Raising questions about whether he identified as a Christian personally doesn't change any of that.
Of course ideas don't emerge from a vacuum, they evolve from existing concept which are modified and combined in new ways.
For example, antisemitism in German society had existed for centuries and later, Luther certainly intensified such antisemitism. In the 19th C scientific racialist theories also became a key driver of anti-semitism, as did the settlement of WW1, and the rise of 'Jewish' Bolshevism.
Hitler relied on all of these concepts in support of his hatred of Jews, so giving Luther preeminence is problematic. I'd say the WW1 + Marxist influences were likely more relevant in his radicalisation than theology or science (as was accepted as science at the time).
Hitler also shared Luther's nationalism, and views on the role of family, but should we assume that he held these
because of Luther?
German society was influenced by Christianity, and Nazism was a product of German society. In this sense Christianity, among other factors, necessarily had some influence on Nazism, and many Christians saw enough in common to reconcile the two or find them mutually supportive (although Lutheran Protestantism was easier to reconcile than Catholicism).
Of certain tenets of Nazism multiple factors supported similar ends, and different Nazis focused on different factors in support of their beliefs:
Antisemitism: religious, scientific, political, anti-Marxist
Nationalism: religious, volkisch, romantic, political
Social/familial: religious, political/anti-Marxist
I'd say the balance of probabilities suggests Hitler's motivations were primarily political and anti-Marxist, rather than theological. It's also probable that some of those who influenced Hitler were driven, in part, by religious motivations.
Hitler's radicalisation doesn't seem to result from a religious epiphany, his inner circle was disproportionately anti-religious compared to the rank and file which seems to suggest religious motivations were not key factors in his worldview. His attitude towards Christianity also appeared to become more negative from the late 1930s onwards, and it seems likely that he viewed its replacement as a desirable long term goal.