Asylum for Homeschooling?

A German couple is seeking political asylum in the U.S., alleging they are being persecuted for their evangelical Christian beliefs which lead them to homeschool their children.  According to this article, German state constitutions require children to attend schools.  Parents who try to homeschool their children can be fined or imprisoned, and even have their children taken away by social services officials.

I find the rationale for this requirement quite puzzling.  At least as explained by the German consul general for the Southeast U.S., as quoted in this article:

For reasons deeply rooted in history and our belief that only schools properly can ensure the desired level of excellent education, we . . . go a little bit beyond that path which other countries have chosen.

Another person interviewed in the article is Bernadette Meyler, Cornell Law School, who suggests

The idea is homeschooling might lead to the emergence of separate societies that would not share the same vision of the (German) state.

I would think that Germany's history would suggest that protection of individual conscience claims would be of utmost importance, even at the possible expense of some "excellence" in education, or a united vision of the State.

Can anyone shed some light on Germany's homeschooling policies, or the likelihood of success of this couple's U.S. asylum claim?