Even within the USSR--let alone the "Peoples' Democracies" where Czech, Polish, etc. continued to be written in the Latin alphabet-- Stalin generally didn't require languages traditionally written in the Latin alphabet to switch to Cyrillic. Thus, Lithuanian, Latvian, and Estonian continued to be written in the Latin alphabet. As for Moldovan, remember that Romanian was written in Cyrillic for centuries (until the mid-nineteenth century). Soviet Karelia after 1940 adopted Finnish written in the Latin alphabet. (Only very briefly in 1937-9 was a Karelian written in Cyrillic the official language of the Karelian ASSR. And even that had a precedent in nineteenth-century Karelian being written in Cyrillic the few times it was written at all. Unlike Moldavian/Romanian and Karelian, there was just no precedent for German being written in Cyrillic.)
Anyway, Stalin didn't want the GDR to be "non-German." He wanted it to be seen as German--the "good" "progressive" Germany, the supposed continuation of the revolutionary tradition of the
German working class, as the GDR Constitution later put it: "In Fortsetzung der revolutionären Tradition der deutschen Arbeiterklasse…"
http://www.documentarchiv.de/ddr/verfddr.html (Part of this was the hope that the GDR could be used for the reunfication of Germany on a socialist basis.) Far from trying to differentiate their language from German, the GDR leaders argued that it was the
West Germans who had departed from the best German traditions in language as in other matters. As that noted linguist Walter Ulbricht put it, "There is a big difference between the traditional German language of Goethe, Schiller, Lessing, Marx, and Engels, which is replete with humanism, and the language as it is used in certain circles of the West German Federal Republic, which is defiled by the spirit of imperialism."
https://books.google.com/books?vid=ISBN0198237383&id=AviTvt-cPaUC&pg=PA64