This is not a free society.
The Wunderlichs simply felt that they could teach their children better. They opposed the idea of being forced to send them to the government-monopoly schools whose power is based on a law imposed during the WWII era. The Wunderlichs are Christian, and preferred that their children receive an education incorporating Christian themes, and devoid of some elements force-fed to German kids in the public schools.
That doesn’t sit well with the German regime, however, which is, by its own admittance, in the business of preventing “dissent,” including the emergence of “separate philosophical convictions.”