The other side is baffled, because they assume that man shall live by bread alone, and bread comes from the government. Christians value freedom of worship, and freedom to raise their children "in the nurture and admonition of the Lord" more than money.
When we lived in Virginia, we simply ignored the system, and operated under the "conscientious objector" category. We did not go looking for trouble, and none found us, thank God.
We have not found the NC regulations to be onerous. THere's only 3 folks implementing 'em! And they are said to be reasonable people. So, we have not "felt led" to make bold stands down here.
(besides, our 18 y.o. son is now attending his first public school, NC State University!)