Nowhere in the Constitution does it actually say that there is to be a separation of church and state. Religions are protected by the First Amendment, which clearly says “Congress shall make no law respecting an establishment of Religion, or prohibiting the free exercise thereof.”
The two key words are "respecting" and "prohibiting."
So the separation of church and state is a very debatable assumption and not a law at all. As our forefathers were brilliant in writing the Constitution and the first Ten Amendments, if they intended there was to be an absolute separation between church and state they would have said exactly that.
For example, in order to prohibit putting a religious article on the lawn of a government building, Congress would have to make a law prohibiting that act, and to my knowledge no such law has been passed. But passing such a law “prohibiting” religious expression might be unconstitutional. Can Congress pass a law “prohibiting” the use of the word "God" on coins or other places?
Atheists have a right to believe that God does not exist, but they can not impose their beliefs on others, as the others can not impose their belief on Atheists. And this is protected by “respecting” and “prohibiting” When an argument is based on “separation of church and state” that argument is standing on thin ice.
The wording of the First Amendment was not to deny or support a belief in God, but was clearly written to prevent the Catholic Pope - but for any other religious group as well - from ruling our country.