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The state has no right to FORCE testing.

The question is can a state FORCE compliance to education standards and testing. Would you agree that the State could force socialist indoctrination or one particular religion? Once you give the state supreme power to FORCE education and by it's standards your right to self determination and thus the right to Liberty and the pursuit of happiness are taken. Rights that cannot be forfeited or taken by State or Fed as they are inalienable rights foundational to the U.S. Constitution, making them Fact of law.

The state can only intervene if life or property is at risk per the rule of law. Children studied at home may or may not be 'harmed' as determined by some abstract social/economic standards (who sets the standards and will you agree when 'they' are diametrically opposed to your way of life?) but the body or harm cannot be produce in fact so the government has no place.

It is Tyranny.

This isn't forced religion (constitutionally prohibited) or socialist indoctrination (violation of free speech and assembly).

But, yes, the State can test if the child knows how much is five times five or that the Earth revolves around the Sun.