They are right if we are looking for the explicit words "separation of church and state".
But what is not explicit is certainly implicit in our foundational documents. See for instance:
but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.
1. From Article Six of the Constitution
2. From The First Amendment to the Constitution
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof;
I think that Article Six and the First Amendment make two things clear.
First: Persons of any, many, or no religions may hold public office and trust in the United States.
Second: The United States Congress is not allowed to endorse any religion, not is it allowed to prohibit any religion.
In other words - government must keep its hands off religious expression, and religions may not make special demands upon government.
Such was the genius of our founders. It's a genius which modern day american evangelicals and fundamentalists do not understand.