Secular education is the only proper way to ensure that students are getting a proper education.
The story of religion in American schools, public and private, is a lot more complex and interesting than you might think.
Public schools were a result of the American Revolution. But this was a very different society. Religion played a much greater role in the lives of ordinary citizens, most of whom were Christian. Disputes in those days, well into the 19th century, weren't over Religious Vs. Secular, but rather sectarian.
Most people do not realize that at the time the Bill of Rights and the Establishment Clause were written, 6 states HAD established religion! The new Federal Government was assuring these states that they would not interfere with state-established religion.
It wasn't until the early 19th century and the Age of Jefferson that the Separation of Church and State became an issue. It was when Connecticut's establishment of Congregationalists were bullying the Baptist minority that Jefferson wrote his famous Letter to the Danbury Baptists.
The colleges which became our Universities were still considered Seminaries at this time, with mandatory prayer. Princeton is a perfect example. Students began to object to the religious requirements. They rioted and even detonated a bomb under Nassau Hall. (To this day, there is actually a crack in the building caused by this). Harvard and Yale also went through a transition from seminary to secular institution. In Princeton, the Princeton Theological Seminary was founded and the college itself secularized.
The Founders had different ideas about religious instruction in public schools, but of course this was not universal. In 1783, Continental Congress produced the Aitken Bible "for use in public schools." The production of this Bible and its stated purpose is recorded in the Papers of the Continental Congress, most notably in the folder "On Locating the Seat of Government," because they were also determining the location of the "Federal City" at this time. The purpose of this Bible was repeatedly stated as "use in public schools." This Bible was produced largely under the influence of the Rev. John Witherspoon, Signer of the Declaration, Ratifier of the Constitution, and President of Princeton. A sidelight: Witherspoon was one of the most influential yet forgotten of the Founders, and the reason he was not a participant of the Constitutional Convention was because he was attending a Constitutional Convention for the Presbyterian Church in Philadelphia that summer!
Benjamin Rush another signer of the Declaration, who also founded the American Bible Society: he wrote an essay "A Defense of the Use of the Bible as a School Book."
https://books.google.com/books?id=xtUKAAAAIAAJ&dq=Benjamin%20Rush%20bible%20in%20schools&pg=PA93#v=onepage&q&f=false
In modern times, we do have Fundamentalist Christians pushing for Bible instruction in public schools. Trump's nominee for Secretary of Education, Betsy DeVos, is among them. But DeVos comes from a bizarre organization called Amway,which scams hundreds of thousands every year. That is where her fortune is derived. Both Amway and the DeVos family advocate not only Biblical instruction in public schools, but promulgate an anti-science pro-Biblical philosophy. Paul Miller, one of Amway's stars, is just one of many who openly advocate this. I heard him in person, and others from Amway, state that Evolution is a scam, the Earth is 6000 years old and that Bibles should replace science books in schools.
This is a perfect example of why public schools must be secularized. Society and America itself has changed since the Founding generation.Voluntary, extracurricular religious instruction should be permitted, and it is necessary to understand the influence and role of religion in history and society, but this must be secular- not an easy task for teachers.