I meant not "everyone agrees with this" but "many people with a wide variety of political positions agree with this". And I didn't intend to imply that everyone [sic] in their programme other than "kill the Jews" is in that category.

What do you mean by a "wide variety of political positions"? Your definition of "Nazi" currently amounts to "supports the parts of the Nazi platform only Nazis support". Now obviously stated this way, it is clearly a circular, hense useless, definition. So we are left with how you use it in practice, which brings us back to "supports the parts of the definition gjm doesn't approve of".

"The state is to be responsible for a fundamental reconstruction of our whole national education program" could, in isolation, mean anything from "we're going to build a lot of new schools and fund a lot of new teachers" to "we're going to close down the education system entirely" via "we're going to turn the schools into brainwashing units"

I don't see the difference between your first and last interpretation. After all if "we" build new school and fund a lot of teachers, "we" are presumably going to have them teach cources on history, social sciences, etc. and do it from our precpective. One could get around this problem by not having education be centralised, but that's not what either the Nazis or Bernie were proposing.