I don't know, to be honest. What if the US allows spanking (not sure if they do or not), and another country has banned spanking (not sure if Germany bans that or not). In the other country this would be considered child abuse, and if the parents refuse to change their ways, child protection services would take away custody of the child after a while. Would that be grounds for asylum?
Or what about that girl who wanted to sail solo around the world in the Netherlands a while back? Child protection is monitoring the case, but if they would not allow it and the parents allow it anyway, they would lose custody too. Would that be grounds of asylum, based on persecution? I think not.
The main difference is that homeschooling per se, or spanking, or allowing solo sailing around the world, aren't basic human rights. In some countries they are rights, in some they aren't. But it's not a human right. All they have to do to keep custody, is follow the laws and not homeschool. Or with the spanking example, to stop spanking.