The issue was the star, Tom Cruise, and his love of Scientology. Though you probably knew Cruise is a Scientologist, you manage not to think about that fact constantly whenever you watch one of his movies. Germany, on the other hand, pays special heed to people's religions. Unlike America's general hands-off policy, Germany regulates religions by formally recognizing some and rejecting others. For many years, they refused to recognize Jehovah's Witnesses as a legit religion, and they consistently do the same for Scientology, calling it a cult and a money-making scam.
If you're going to throw those accusations against any group, Scientology's a good candidate. But even so, Germany goes a little far with their anti-Dianetics crusade. The country labels businesses owned by Scientologists, makes government employees declare whether they're Scientologists, and even got Microsoft to remove their disk defragmenter from Windows when Germany discovered a Scientologist had designed it. When Valkyrie came to film, the country used Cruise's Scientologist status as a reason to block them from filming in several sites.
In the end, the producers got the Defense Ministry to walk back their decision, but for a while, the government argued that movie was a Scientologist plot to legitimize their cult with German children by appropriating German history. Officials compared this film to Nazis putting on the Olympics and compared Cruise to Joseph Goebbels. Which is a hyperbolic jump at the best of times but is an especially strange fit here since this movie features the actual Goebbels as a villain, and the main plot is Cruise's character trying to kill Hitler. Of course, people have also compared Germany's discrimination against Scientology to something the Nazis might do, and anyway, you know who else tried to kill Hitler? Hitler.