Not necessarily. It could just be the leftist media bias.
Have you ever read this?
'A Wall of Separation' - FBI Helps Restore Jefferson's Obliterated Draft - Library of Congress
It certainly clears up a few misconceptions.
Nice article, however;
Just as the concept, separation of church and state is not in the Constitution or the Bill of Rights, yet is drawn upon as the outside authority for the State. Further, there appears to be a movement which is attempting to remove the underlying concept of inalienable as an individuals right based on what the Federal Government permits; instead of being constrained or restricted.
If the original intent is subject versus citizens, well then an individuals rights are subject to the States desires this is what separates the French Constitution from the U.S. Constitution.