Setting Nazis aside, Germans are used to having a single source of correct grammar and vocabulary.

The first Duden was published in 1880 and helped standardize German language a lot, even though local accents and dialects still persist. But speaking in dialect is considered somewhat low-brow in German language space, unless you are Swiss; even there, people will code-switch all the time.

(E.g. during class, both the professor and the students would speak High German, but during recess, they would switch to Swiss dialect.)

A rural language of peasants who do not use even old tech such as newspapers and radio and reside on a huge territory will necessarily diverge into a barely mutually intelligible family of local dialects, at least in the spoken form. Basically the Medieval or Early Modern standard situation.