I don't know if this stood up in the (civil) courts, but the New York legislature's solution was to include in the divorce law a requirement that, in order to get a civil divorce, both parties must testify in court that they had removed any impediment to the other person's remarrying. I'm not sure of the exact phrasing. It doesn't explicitly mention religion, but it means that if the couple were married under Jewish law, the man has to issue a get before the civil divorce can be final.