Note the phrase "
oath or affirmation"; unless I miss my guess, I'd imagine they're referring to the
Quaker practice of refusing to take oaths, but instead to "affirm" that they're telling the
truth. In any case, it certainly also gives
atheists equal status with religious people in this context.
This seems to open some big, wide holes in the theory that the
framers of the
Constitution intended to confer some kind of
special status on
fundamentalist Protestantism.