Actually I have never seen much Nazi propaganda which emphasize the Judaism. Doesn't mean they didn't care of course.
However the way I see it Nazis were mostly concerned with what they deemed the backstabbing that led to Germany capitulating in WWI. This angered nationalists greately.
This happened because of a socialist led revolution in Germany which formed the first democratic Germany: The Weimar Republic. This caused Nazis to deeply hate socialism and liberalism.
People like to find scapegoats. Somebody to blame. The idea that socialism and liberalism was un-German but originated with Jews began to take hold. One can see how that would work out. Many intellectuals including liberals and socialists where in fact Jews. Thus by mixing in Jews as being both evil capitalists, bankers, socialists, communists and liberals against he normal "decent" German they had a perfect coctail of hate.
My impression was that religion was not a big part of this. The struggles of the 1930s was primarily between different political ideologies such as Fascism, socialism, liberalism, conervatism etc. Socialism became associated with Jews.
For this reason when Nazis labeled somebody a Jew, it did not always literally mean a Jew. At times it simply meant a socialist. It means somebody "poisoned" by Jewish political thinking and ideology.
Albert Einstein is perhaps one of hte most famous Jews in modern history and he was an ardent champion of socialism. A lot of this mixing of politics and racism seems to be completely gone in American discourse on racism. I suspect there is an interest among the liberal American elite to only make it about skin color and leave class and politics out of it.
Here in Europe it is still very much alive. Our home grown right-wing Neo-Nazi Anders Behring Breivik. Shot dead and blew up around 80 people. He did not target none whites. He targeted social democrats/socialists. Nazi racism is strong tied to hatred of socialism and liberalism. Jews are hated as they are seen as originators of these ideologies.