True. This happened as a result of one of a series of 20th Century Supreme Court decisions that turned the original intent of the First Amendment on its head and created the current federal antipathy to religion.
Actually, that one is in the Constitution itself-- any time it mentions swearing an oath (oath of office, sworn affidavit needed for a search warrant, etc.) it says "oath or affirmation." The "affirmation" option was put in for the benefit of religious dissenters who refused to "swear to God."
Again, whether you believe that it is right or not for a state to require that a witness demonstrate competency by declaring a belief in God is beside the point. What I am countering is the fraudulent revisionist history that asserts that the federal government had an antipathy for religion from the very beginning.