But this fact won’t stop southern christians, who feel it is their duty — as christians — to make the United States “a godly nation” in their eyes.
It’s Time to Start Calling Evangelicals What They Are: The American Taliban
JC Weatherby
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The document quoted, while it does recommend “posting the 12 commandments at public schools”, it also states

“Just as the Christian gospel was designed to succeed by acclaim, not by coercion, so must be our every effort.”
“… the deficiencies of government-run secular education and provide an attractive, superior alternative”

So, I don’t think they’re advocating for theocracy. Just advocating for supporting parent’s choice to send their kids to private Christian schools.

Keep in mind that colleges tend to better accept kids from public schools than private ones, so they’ll be sending their kids to private schools at the cost of opportunity.