From my recent trip to Germany and staying with a family, the elderly man who we stayed with doesn't speak Hochdeutsch, but instead Plattdeutsch.
He told us how only Hochdeutsch is used in schools and it's what all the young people in the area speak now, instead of dialects from the area, and that when he was at school decades ago, it was entirely different with only Platt used for where he was.
As a side note, this is in the region of Niedersachsen, south-eastern Niedersachsen.
So with the Nazis having their view on people, what was their approach towards non-standard dialects spoken by them? Did they want/try to remove them in favour of Hochdeutsch, or were they seen as equal to Hoch as it was still Germanic? Was a sidelined view taken where Hoch was preferable but it wouldn't matter if non-standard dialects were used?
The answer doesn't have to be limited only to Northern Germany, as Southern Germany and Austria are just as relevant.
I found an article (in German) about Low German Nazi Propaganda here. I assume that Plattdeutsch was not banned nor removed; I guess that the prevalence of Hochdeutsch over Plattdeutsch has deeper roots and Nazi power did not substantially affect this. Hochdeutsch has been the standard written language for centuries, and I think already in the 19th century Imperial Gemany favoured the diffusion of a common language through the educational system, just like other countries did.
I do know, however, that another totalitarian state fought a war against dialects and idiotisms: Fascist Italy. Here you can read something about that (in Italian). The Fascist regime wanted to remove any centrifugal force from Italy: it oppressed linguistic minorities, and tried to contrast the use of dialects. Note however that, even if with less dureness, this was the common approach towards local languages even in democratic nations: see for instance the French war on Provençal.
This measures however did not work. The real threat to dialects in Italy (and Germany too I guess) was brought after the war by mass media.