Vouchers have been ruled constitutional by the U.S. Supreme court.
If state constitutions require the existence of collectivist, socialist-funded, voting mob and comrade committe managed ( school board, prison-like, government schools, then there is an internal conflict between compulsory government schooling and the U.S. First Amendment and any state First Amendments.
ALL government schools are in complete and utter conflict with the First Amendment and freedom of conscience.
ALL government schools trash free speech, free press, free assembly, free exercise of religion, and establishment of religion.
As far as vouchers being constitutional, I have a problem with that. In my state there are several muslim charter schools that the children get vouchers for. So my tax money is going to educate future terrorists.
I also understand that in your world view there is no neutral. As is the case for many of the world religions. We do though have a secular government and based on that the best that government can do is be neutral.
This of course wasn't a problem for this country for the first 100 years because majority of Americans were some denomination of protestant.
The history of prayer and bible study in school is very interesting. The first group to attempt to get bible reading out of schools were the catholics in the 1850’s. This is because most schools were using the king james version of the bible. They actually won their case in front of the Wisconsin supreme court and bible reading banned in 1890 in that state. However, in most states they were not successful and in Philadelphia there was actual violence against catholics for their perceived attempt to stop the bible readings. This is one of the reasons that there are so many private catholic schools.
Fast forward to today were we are a much more diverse religious nation. Protestants now make up only 51% of the religious in this country. (CIA World factbook) So even though some people may see neutrality as an impossibility I believe the majority of Americans would support it.
Also remember that our constitution allows us to violate 7 of the 10 commandments.