Parochial schools are religious based schools. Teaching religion is their business.
The federal Department of Education, which took the reins away from the individual states, and their particular syllabi, oversees the secular instruction of the pupils, to federal government standards, sans religion, as per the 1st Amendment.
IF, my tax dollars are being argued to teach Christianity, and that alone, as some form of “religious training” in the federal schools, then I desire to see Taoism, Buddhism, Shintoism, as well, while excluding Judaism (parochial school exists), mohammedanism, a political theocracy in direct opposition to the U. S. Constitution. It’s all or none.
That is the problem with false religions, they assume the same rights as true religion, and consequently sow much confusion about who God is and why we belong to Him.
The public education system in this country was founded because the free-masons feared that the Catholic school system was in due time going to make most of the citizens Catholic.