mw13 I did misunderstand you. Thank you for explaining.
Regarding your second question: I’ve met some charedi people who think moisdes chinuch in E”Y should have more secular studies than they do today. But they said so simply because they found it reasonable, not because they thought we have obligation to the medina.
If the Education Ministry made some demand that everyone could agree was unreasonable (for example that all schools must be co-ed) I doubt you’d find any charedi who’d say we should listen to them just because they give us money.