First the Bill of Rights, as passed by Congress and the States only apply to the Federal Government. That is clean by the worlds used in the Bill of Rights and the intention of Congress and the States when it was passed.
This changed when Congress adopted the 14th Amendment which extended "Equal Protection of the Laws" and "Due Process" to the States. Even after the 14th was passed, the Bill of Rights was held NOT to applied to the states UNLESS we are talking of Equal Protection of the Laws (Which the Supreme Court then restricted to rights in the Constitution itself NOT the Bill of Rights) OR some sort of denial of Due Process of Law.
In 1905, in the infamous Locher vs New York Case, the Court adopted the concept that Due Process was broader then what happens at trial, but it would be a violation of the Due Process Clause if the State would force a person to violate a right protected under the US Constitution. In Locher the issue was the right to enter a Contract, a Right stated in the Constitution itself NOT the bill of Rights. The Court ruled that it was a denial of Due Process for a State to prohibit a worker to enter into an employment contract to work 24 hours a day at starvation wages (Thus striking down a Minimum wage and Maximum hour law of the State of New York). Thus was born the "Substantial Due Process" Concept.
After WWI, the "Substantial Due Process" concept was expanded to included Freedom of Speech and Assembly. IT was soon expanded to Religion and other groups on the grounds it was a violation of Substantial Due Process for the State to prohibit speech and people to assemble. Thus the Bill of Rights was equaled to the Right To Contract.
The problem with this trend is that in 1938 in the case of Jones and Laughlin Steel Company vs NLRB, the Court over turned Locher and said the States and the Federal Government could put restriction on one's right to contract as to wages and hours. Thus the case that set up the incorporation of the Ten Amendments was struck down as no longer good law, but it is the case that the whole concept of incorporating the Federal Bill of Rights to the States is based on.
Remember the concept of Separation of Church and State is based on a letter of Jefferson, but not a letter in regards to the Constitution but how government SHOULD be set up. The concept, in the letter, is NOT based on anything in the Constitution nor any comments on the Constitution of his time period. It is more a comment how things should be NOT how there were.
Now, the Supreme Court has long ruled that the Bill of Rights is incorporated to the States via the Due Process Clause of the 14th Amendment. It is part of the policy of the Supreme Court to make Civil Rights an important issue for the Court, as opposed to the Supreme Court traditional policy of primarily protecting property rights. Prior to the Supreme Court decisions starting in the 1920s, the court REFUSED to protect People Civil Rights, leaving such protections to the Congress and then restricting such protections if such protections interfered with property rights.
My point here is the Court has long ruled the Bill of Rights are incorporated to apply to the States via the Due Process Clause of the 14th amendment, but you can make a valid argument in the from how is the Freedom of Speech a Due Process issue? If the state say I can NOT make a speech in the middle of the Street, how are my rights to Due Process affected? Due Process is HOW the Courts handle a case, NOT the underlying law. I can see have my case heard by a Judge and Jury. I can still appeal any adverse decision. All of that is Due Process, but how is how and when I make as speech an issue of Due Process?
Separation of Church and State is even an easier subject, you do NOT have to worry about the issue of a Law saying you can not do X, thus making X illegal and giving you no chance to do X (The classic case of Substantial Due Process claim i.e. the law prohibits me from doing what I want to do without a chance to give me a chance to argue why I should be able to do what I want to do).
A law authorizing a State Religion does not prohibits someone from refusing to join that Church. Thus, the person who does NOT want a State Church can form their own, or protest the state church. Thus such a law does NOT prohibit someone from doing X. The law just provides funds and other benefits to the that church. This type of case avoids the issue of someone being prohibited from doing something, if you do not want to join you do not have to. Taxes will go, but taxes go to many places people do NOT want their taxes to go (For example the War in Iraq and Afghanistan). How is this a violation of a person's right to due process?
Now, the Courts have ruled BOTH of the above examples are violation of the 15th amendment's Due Process Clause. The Issue of Freedom of Speech and Assembly is easy, for in those cases the States were prohibiting people from doing something, that they had no where else to go to perform those actions.
As to funds to churches, the Courts have long ruled that Churches can NOT get tax money except in certain limited circumstances (i.e. where the Church is in the same line as secular providers for the same service). It is a harder call, but that is how the courts have ruled i.e. it is a denial of Substantial Due Process for a State to provide Money for a Church for Church related duties that had nothing to do with the state.
The Courts have also accept as a violation of Due Process for the State to set up religious displays unless such displays can be set up by anyone (and even then restricted i.e. has to be neutral, no nativity scenes for Muslims, Jews and atheists have no equivalent observations).
Given the above, all I am pointing out is that the whole concept of Separation of Church and State is based on the Incorporation of the Bill of Rights via the Due Process Clause of the 14th Amendment. As such it is built on quick sand, for how is the rights in the First Amendment due process rights? The Courts have said they are, but you can make a good argument that they are not.
If you want to read the 14th Amendment:
Amendment 14 - Citizenship Rights. Ratified 7/9/1868.
1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.(I am excluding paragraphs 2,3 and 4, for those are US Civil War specific clauses)
http://www.usconstitution.net/const.html#Am14Locher vs New York:
http://en.wikipedia.org/wiki/Lochner_v._New_YorkThe actual case:
http://supreme.justia.com/us/198/45/case.htmlNLRB vs Jones and Laughlin Steel Corporation:
http://en.wikipedia.org/wiki/National_Labor_Relations_Board_v._Jones_%26_Laughlin_Steel_CorporationActual Decision:
http://supreme.justia.com/us/301/1/case.html