America was founded by mostly Puritan [Christian] pilgrims and pioneers who embodied their Christian beliefs and doctrines into non-sectarian [non-denominational] government documents and charters, besides using The HOLY BIBLE as their main textbook in their early public schools.
Not everyone was an evangelical Protestant Christian, of course, but those who were not (be they Jews, eastern-religion asians, greedy prospectors or trappers or saloon-frequenting sometimes-drunken poker players, etc.) respectfully feared and reverently complied with those founding fathers and mothers were were actual Christians and not merely deists.
Throughout the history of America, up to and including the present, the traditions of patriotic Christians, their Biblical teachings, plus the extensive and pervasive influence of such is rather obvious.
Therefore, it is a "no-brainer" as to the question of whether or not government, their congress, and their agencies should not only not establish anti-Christian religion....but also not prohibit the free exercise of genuine Christian religion by the law-abiding who practice it.
That includes the issue of vouchers for religious education.
Now, not all parochial schools are worthy of being funded by government vouchers, because some religious schools are rife and reeking as hotbeds of anti-Scriptural heresies - skilled in instilling a subversive assortment of doctrines of demons into young minds which should not be so polluted and defiled. Indeed, this webauthor (who could not afford the high costs of questionable-dogma parochial colleges) nevertheless was fortunately introduced to the great sacred masses and requiems of the clasical composers at a "secular" [public] university!
Not all need to go to a four-year college or university, since many instead choose vocational schools after graduating from high school. But everyone should be required by law to be a high-school graduate in order to safely and successfully exist in modern English-speaking basic-math-and-science society. So government need not fund post-high-school educational institutions.
From K through 12, however, government has a compelling interest to properly apportion educational directives for the well-being and security of communities and neighborhoods within their territory and jurisdiction.
In accord with the Christian heritage and traditions of America throughout the past two hundred years, the singular Judeo-Christian Holy Bible - upon which such Christian history and actions have been and yet are based - is the standard upon which to draw the line as to what are bonafide parochial schools contrasted with those which are not so qualified. The common-denominator English translation of that Bible is the [non-apocryphal] Protestant King James Version which can be supplemented by the [non-apocryphal] Catholic Douay Version.
[The reader will notice not only the understandable and legitimate omission of the apocrypha, but also the Koran (Qu'ran), Book of Mormon, Egyptian Book of the Dead, Robert's Rules of Order, the Code of Hammarabi, Mein Kampf, and more].
Because election-day ballots contain propositions for increased school levies supported by more property taxes from homeowners and corporations (not state income nor sales taxes), those parents who sign a government-issued affidavit stating that they promise - under penalty of perjury - to send their kids to approved-religion K-through-12 parochial schools (NOT the Church of Satan nor the Islamic School to Train Terrorist Pilots) should be sent back a government statement indicating how much less they have to pay in property taxes than their neighbors who instead choose to send their kids to public schools. That is so that such religious parents do not have to pay double (that is: BOTH for parochial-school tuition AND for public schools they do not use and do not directly benefit by). With property tax reduction, no special vouchers are necessary.
Those parents who choose to send their kids to public K-12 schools should be send a required-reply government questionaire as to which multiple-choice-listed books of the 66-book (KJV) Holy Bible they want read to their children. [It is assumed that most will check off Proverbs and Ecclesiastes and few check Chronicles]. In any case, public-school teachers are mandated to read a chapter a day to an opening-assembly morning gathering of public-school students for those willing to participate (instead of excusing themselves to study hall) before the start of classes.
Clearly, such holy and sensible education goes beyond the insuffient quasi-morality of Leave It To Beaver, Lassie, The Lone Ranger, Bonanza, Gunsmoke, Little House on the Prarie, and many others of the same ilk.
The short and pertinent daily morning Bible readings to public-school students would go a long way to alleviate, suppress, stifle, and stop bullying, stealing, obscene language and misdress, graffiti vandalism, sexual molestations, intoxication with narcotics, smoking addiction, and after-school drive-by shootings. The words "value, honesty, respect for parents, pride, esteem, endeavor, determination, patience," and other could-go-either-way words would be given the right meaning for genuinely-noble purposes and actions.