It is well-known that the First Amendment to the U. S. Constitution in the Bill of Rights says, "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof".
Originally, these two statements were seen as two sides of the same coin: for government to establish a particular religion meant that members of other religions would be prohibited from practicing their own. So government should not have the power to prevent people from practicing their religion by establishing one religion as the official one.
For the last several decades, however, the courts have been interpreting the First Amendment in such a way that these two statements are mutually exclusive. An "establishment of religion" now means that any collection of people who have any ties at all to government do not have the right to express their religion in that setting. This leads to absurdities such as students being told they cannot engage in religious activities on public school grounds. How can this possibly avoid the charge of "prohibiting the free exercise" of one's religion? How does it amount to a government "establishment of religion"?
So I think it's necessary to understand the First Amendment in such a way that these two clauses do not contradict. I think this is achieved by understanding it as saying that no one should have restrictions placed on what they believe (and how they express these beliefs) about subjects that are usually understood as religious in nature: the existence and nature of God; the possibility of an afterlife; the purpose and aim of the human being; etc. (Note that these subjects are just as much philosophical as they are religious.) This means that those who want to express a belief that God does or does not exist should not have any restrictions placed on this expression by the government unless such expression prevents others from expressing contrary views, or it becomes dangerous to society. Of course that last one is probably going to be different for everyone.
In other words, the "establishment of religion" should not be understood to mean that any social group with ties to government should not have the right of religious expression in that forum. Rather, it should mean that no opinion regarding a religious subject -- such as whether or not God exists -- should be prohibited from being expressed in that forum. Neutrality on a subject is not achieved by prohibiting any attempt to address it; it's achieved by allowing all views to be expressed.
Obviously this is a complicated issue that a knee-jerk reaction can't do justice to. We have restrictions made on all of our freedoms, including our most basic ones of speech, expression, and religion. Yelling "Fire!" in a crowded theater that is not on fire is not protected free speech for example. I suspect that most of this issue is going to be argued on the level of where the line should be drawn, not whether a line should be drawn.
(reposted from OregonLive)