When governments give you something, it is usually because they want something in return. The zionists give the hareidim money because they want them to “behave”. The Americans give the Israelis money to make sure the Americans will do their bidding and not get in America’s way (with the added benefit that American aid is designed to reserve American jobs by requiring the Israeli to cripple their own military industries).
If Israeli hareidim want to free of zionist control, they need to reject zionist funding. If the Israelis want to be independent of the American government, they need to turn down foreign aid. Neither is likely to happen.