I'm not sure how the judge can ensure the requirements for a juror can be met if he has to follow the requirements of the second paragraph. Seems like a bit of a contradiction to me.
The wording implies to me that a juror can be judged incompetent for not believing in God, but doesn't have to be. Maybe I'm misinterpreting the meaning of older texts though.
If the idea of swearing to God bothers you, don't think of it as actually swearing to God. Think of it as a formalised piece of language simply meaning that you're making a serious promise.
The long influence of Christianity on English and American culture means that our language is riddled with religious formulations we now use devoid of religious meaning. I don't believe in God, and yet I entreat Him to bless people when they sneeze; and cry His name in anguish when frustrated. I warn people away from schadenfreude by reminding them that only God's grace keeps us from a similar fate to those unfortunates we mock, and I entreat the aid of Heaven when things look bleak.
It all seems less offensive when viewed this way, and even kind of nicely quaint.
Edited by caffeine, : To give a subtopic title