In order to answer this question, I would want to know why one was opting out of having the state involved...
I do know of some cases where there are two elderly people who, if they marry according to the state, the Soc Sec. Admin. would so cut back on their benefits, they couldn't afford to live. In cases like that, there are some churches willing to give the couple a Christian wedding and marry them in the church...even though in the eyes of the state they are just living together. And I don't really have a problem with that...
But, if two people want to marry outside of the state in order to defraud or because the state won't recognize their union due to things like, oh say, bigamy, polygamy, homosexuality...well then there are some pretty big things to consider here.