Why preposterously?
You can teach your children whatever weird shit you want. What you cannot do (in Germany) is take them out of school, where they will also be taught what everyone else is taught, including sex-ed, history, comparative religion, etc.
EDIT: correction, it's not an obligation to visit a public school, it's an obligation to visit a permissible school (there are private ones, but homeschooling does not constitute a permissible school).
I could see how one could reasonably view this as some sort of political or religious refugee, depending on context. They are, at the end of the day, facing punishment for a practice a typical American would find acceptable if not a little strange.
Sure, we could accept Americans as "politically persecuted", because highways in America have speed limits. But we choose not to.
At some point you need to accept that not every difference in laws is persecution. That not every difference in law means that the other one is doing something wrong.
Alas, the US Supreme Court feels similarly when its conservative wing always dismisses all analogies and examples abroad as obviously uninteresting. I think "our SCOTUS" gets this balance right, or at least more right, when it differentiates between "would not constitutional in Germany, but is a valid viewpoint" and "would not be constitutional, and is so far beyond the pale that there cannot be an accomodation".
An extradition case starring an American from some years ago is a prime example for this differentiation, in my opinion (anyone interested in reading a summary?).
Germany ranks highly in measures like the World Index of Moral Freedom, the Freedom in the World rankings, and the Freedom of the Press report. If Germany's citizens are entitled to asylum, is there any country whose citizens aren't?
