The Romeilkes have circulated a petition claiming persecution in Germany based on that country's failure to allow homeschooling. Based on this, they claim they must remain in the US to avoid persecution.
While it may be a bad thing that Germany doesn't allow homeschooling, it is not persecution. First, Germany allows students to attend any established school, whether public or private. Second, the Romeilkes are members of the European Union, and as such are free to live in any other country in the EU, most of which (e.g., German-speaking Austria) recognize homeschooling.
Thus, just as an American unhappy with California's tax laws need not seek refuge in Mexico to avoid them, there is no need for the Romeilkes to request special treatment from the US in this case.