The winner here is reasonably clear. The most widely owned book on GoodReads which is set in Germany, and the second most widely owned on LibraryThing, is also the book most frequently tagged "German" by the users of both systems. It was published in 2005, and made into a 2013 film. The narrator is a supernatural being (or perhaps a primal entity), but the story is otherwise grittily realistic. It is set in Munich during the Second World War. It is:
The Book Thief, by Markus Zusak.
As mentioend above, there is one other book with a German setting, also during the Second World War, which is owned by more people on LibraryThing. However, the German setting is only one passage (admittedly the most memorable one) in a book which also passes through wartime Belgium and Luxembourg, 1960s America (it was published in 1969) and an alien planet where humans are displayed in a zoo. It is, of course:
Slaughterhouse-Five, or The Children's Crusade: A Duty-Dance with Death, by Kurt Vonnegut
The third, fourth and fifth most frequently tagged books on both systems are the same, though in slightly different order. Third on LibraryThing, fourth on Goodreads, is another Second World War novel, published in 1995 and made into a film in 2008. It is:
The Reader/Der Vorleser, by Bernhard Schlink
Third on Goodreads, but fifth on LibraryThing, is a novel of the First World War rather than the Second. Published in 1928/29, it was adapted into a famous film with the same title in 1930, and was of course burned by the Nazi regime. It is:
All Quiet on the Western Front/Im Westen nichts Neues, by Erich Maria Remarque
And in fourth place on LibraryThing, fifth on GoodReads, is a historical work published in 1960, a comprehensive effort to address not only the Second World War but also its causes:
The Rise and Fall of the Third Reich: A History of Nazi Germany, by William Shirer
Apologies to Günter Grass, Hermann Hesse and Thomas Mann, who I had hoped to see doing better.