They aren't German. People don't bother to check the facts.
The Queen has German ancestry. Like all other royals in Europe, she also has French, Italian, Scandinavian, and other ancestries. She is, however, more English than German, far more English than anything else. The German contribution came along relatively late in the history of the monarchy, and the Hanoverians were, like Elizabeth herself, descendants of a long line of English and Scottish monarchs. That's why George I was offered the throne -- that and the fact that he was a Protestant.
I might point out that the Anglo-Saxons were a Germanic people -- you didn't know that? -- that they immigrated to the British Isles from elsewhere, and that they intermarried with other peoples. Alfred the Great's grandmother, for example, was a Frankish princess.
There has never been a "purely English" king. Never. You need to look into this more closely.
In any case, when you, your parents, and your grandparents were born, raised, and educated in a given nation, you are NOT "German" or a native of whatever country some of your ancestors might have happened to come from. I am an American of Anglo-Scot ancestry on one side and Franco-German ancestry on the other. That doesn't make me British or French or German. I'm American.