Bothwell can't be forced out of office over his atheist views because the North Carolina provision is unenforceable, according to the supremacy clause of the U.S. Constitution. Six other states, Arkansas, Maryland, Pennsylvania, South Carolina, Tennessee and Texas, have similar provisions barring atheist officeholders.
In 1961, the U.S. Supreme Court reaffirmed that federal law prohibits states from requiring any kind of religious test to serve in office when it ruled in favor of a Maryland atheist seeking appointment as a notary public.
But the federal protections don't necessarily spare atheist public officials from spending years defending themselves in court. Avowed atheist Herb Silverman won an eight-year court battle in 1997 when South Carolina's highest court granted him the right to be appointed as a notary despite the state's law. From Raw Story
I can't think of a better working demonstration of just how far the Religious Right would like to go.
This is also a nice little glimpse of what "states rights" actually can mean. It means the "right" of states to discriminate against unpopular minorities.