Most of the posters here seem to be a tad ignorant of basic history.
When the Medinah was founded the Chilonim acknowledged the need for the majority of Chereidim to at least refrain from publicly protesting them. THe Charadim were extremly apprehensive of the proposed government for fear they would seek to impose their ideology on the Chareidim. So in a series of meetings they hashed out a compromise based on four core areas.
One of them was that the Chareidi chinuch insitutions would be completley free of government inteference.
This was a bedrock principle that the State of Isreal was founded upon.
Now of course the elementry schools in Isreal are more or less “public schools” that is becuase the State of Isreal is more or less socialist in nature.
When you go to the store you pay about 17% Vat everyone must pay it, including chareidim.
As such while yes they are more or less free because of the socialist nature of the economy, any attempt to intefere in the chinuch of the chareidim is a violation of the principles upon which the Chareidim agreed to the founding of the State of Isreal.