Um...I'm kind of speculating about this, and if anyone from Germany could back me up/correct me on this, but isn't homeschooling in Germany a lot less feasible due to their education system?
I mean, you start specializing at the age we're just going into high school. Can someone who went to the Realschule can you give a gymnasium education?
I don't think so. I would even argue, that someone who only went to the gymnasium would not be equipped to give a gymnasium education. The problem starts with the lesson during which the parents slept in school, goes on with different specialization (someone who went to a school that taught Latin and Ancient Greek as languages might not be the best person to teach English and French) and ends with the different educational standards between now and then (and due to federalism, between different states).
If you went to the Gymnasium can you give a Realschule education?
Probably for most subjects, but there are subjects, where someone who attended a gymnasium is clueless about.
Of course parents could try to learn about the subjects they know nothing about to teach them to their children. But children tend to notice and get frustrated, when the teacher is ahead exactly one lesson.
How can a University effectively assess your abilities if you've never been to either?
I would probably work like it works now with private schools approved, but not recognized by the state: The pupils have to make their final exams at a state school and the grades from that exam will be the ones that count.
However, the only thing required to attend most German university programs is that you have graduated from a gymnasium or an equivalent school. There are a lot, where everyone who has that and applies is accepted. Thus they don't need to assess your abilities before hand, they just make the program hard enought that you'll leave if you don't meet their standards.