It is convenient and comforting to divorce Nazi antisemitism from 1,000 years of European Christian antisemitism. A shame that it doesn't fit reality.
I don't want to deny that there was some kind of relationship between some strand or other of Christian antisemitism and Nazi antisemitism (I'm inclined to think that the Germans were open to Nazi antisemitism because of the pre-existing Christian antisemitism), but it's simply not true to say that Nazi antisemitism simply was Christian antisemitism.
That's not true. Yes, I'm sure that the Nazis occasionally appealed to Christian themes, but if you look at the fundamental reasons why they were antisemites, their antisemitism was profoundly secular and socialist.
It's not even just reducible to Martin Luther's "They are plotting against us and are going to kill us and take our property."
The Nazis thought of the Jews as rootless international parasites who would enter into a host nation, and yet, never actually become an integrated part of that host nation. Yes, a Jew might take on the mannerisms, the dress, etc. of a German, but the Jew would never be, nor would he ever think of himself, as a German, but a Jew, nor would the Jew ever really enter into the common life of the nation, e.g., by engaging with the other German "plebs" in manual labor. No, they thought that the Jew is inherently a merchant (read: huckster), a banker, etc. In a word, they thought that the Jew was a naturally grasping sort of fellow, always grasping at money, power, influence, etc., without having any real ties of blood or soil (for, they would say, this rootless international profiteer would live one day in Vienna, another in Prague, another in London, since he conducts his business everywhere, without regard for national borders) to the nation in which he was operating. As such, the Jew, while seeking to exploit his host nation, could never truly have the interest of his host nation in mind, but only the interest of himself and his fellow Jews (thus the reason, they would say, that the Jews, as a whole, were not as impacted by the Great Depression and the economic troubles that followed the end of WWI).
And if you wanted evidence of this, they would point to international banks like the Rotchschilds bank.
If they were alive today, they would doubtlessly have pointed to Goldman Sachs.