Apparently nuns do teach in public schools.  At any rate, the ruling and an earlier ruling in Baden-Wurttemberg both specifically mention nuns' habits, it's not just something I made up.

Hijab almost always demarks a separation from western values

Why?  How?

it is quite common in Europe for brothers and father to require of their sister/daughter to wear this, and at age of 12 or 14, will is irrelevant as well.

And as I keep saying, if that is true (and I have been presented with no evidence of it here) then the girls of whom it is true almost certainly have other issues at home that are more significant than what they wear on their heads.

try integrating into Western society properly wearing hijab - it's not going to happen.

Apparently because "Western society," whatever that is, doesn't want it to.

All men and women are equal, regardless of race, and this strange custom creates two problems - demarcation of gender, and demarcation of creed.

If all men and women are equal, regardless of race or other factors, then why does it matter if a woman "demarcates" herself as belonging to a specific group?  If she's required to disguise her identity in order to get a job, then she's not really equal.  Why not just make everyone dye their hair blonde and change their names to Inga?

Being different is not a crime.

The Bavarian law is discriminatory, full stop.

It saddens me to see otherwise sensible people arguing that it's OK to discriminate against some people because "it's for their own good."