Right now, seven states still have laws on the books banning atheists and non-believers from serving in public office in those states. This is 2022! This despite a SCOTUS ruling in 1961 saying states may not maintain a "religious test" for holding public office. What were those seven states? Maryland, Arkansas, Mississippi, North Carolina, South Carolina, Tennessee, and Texas.Do you have examples where this was actually applied and required in real people running for office? It looks like the organization is digging up 200 years old law and wanting them gone for lack of any real problem to be addressed.
You see the claim was that atheists could not hold certain jobs. Now if those ancient laws on the books are never enforced, then that claim is untrue. That there is a law written on a piece of paper does not mean those laws are applied. So I am asking for the name of a person who was denied a government job because they are an atheist and that is the reason given as a law is supporting that decision. A law from 1776 totally ignored does not count.
Now, the laws are unenforceable because of the SCOTUS decision, but before 1961, the laws were indeed enforceable. In Section 2 of Article IX of the Tennessee constitution, for example, "No person who denies the being of God...shall hold any office in the civil department of this state." This was probably influenced by John Locke, who stated poisonously, "Those are not at all to be tolerated who deny the being of a God. Promises, covenants, and oaths, which are the bonds of human society, can have no hold upon an atheist."
Now, you want a specific example? In 1992, Herb Silverman, an atheist activist and math professor, was denied a position as a notary public because of a ban in South Carolina. He had to sue the state before he could hold the position. In 2009, Cecil Bothwell won his city counsel race in Asheville, North Carolina, but his opponents cited the anti-atheist law in order to try and deny him his seat.
EDIT: But someone will say, "The laws are unenforceable, so it doesn't matter." What if we had an unenforceable law barring African Americans from holding public office? Would that be a problem? Of course. Same as when we have an unenforceable law barring atheists from holding public office.