Not necessarily.
If the local school board is approached by the citizens of a community petititioning them to teach ID along with evolution in science classrooms, it is in no way an imposition of a 'system of government.' The curriculum is coming from the will of the people. Eliminating the Department of Education (which I would love to have happen, since it is the source of most of the liberal agenda forced on our local schools) would not change the fundamental issue at stake here.
And, forgive me, but it is way different than having them teach Chinese or roofing. It is a fundamental right of the citizens of a community to have students taught both sides of this argument, rather than having one side forced down their throats as fact, when it is not.
Your local school board is a government entity. Its members are either elected by the voters, just as your city, county, and state official are, or they're appointed by some other government body, such as your county commissioners (or local equivalent). When the school board, or the state Department of Education, sets curriculum standards, that is an action of government. The probability of every resident of the community's agreeing on what should be taught (and how, using what materials, etc.) approaches zero.
It is a fundamental right of the citizens of a community to have students taught both sides of this argument, rather than having one side forced down their throats as fact, when it is not.
I don't think there can be any "fundamental rights" to a government service's being delivered in a particular way. The deal with government is that the government forces all taxpayers to contribute to the cost of a good only some want, and in return, the consumers lose control over the nature and quality of the good.