The principle is that a Muslim only resorts to a Muslim Judge or any suitable deputy in the event of a conflict. However, and due to the absence of an Islamic judicial system in non-Muslim countries, it is imperative that a Muslim who conducted his marriage by virtue of those countries' respective laws, to comply with the rulings of a non-Muslim judge in the event of a divorce.
Since, the laws were accepted as governing the marriage contract, then it is as though one has implicitly accepted all consequences, including that the marriage may not be terminated without the consent of a judge. This case is similar to that in which the husband gives authority to the judge to do so, even if he did so implicitly, and which is considered acceptable by the vast majority of scholars.
The principle of Islamic jurisprudence applicable in this case is that whatever is normal practice is similar to a contractual agreement. Also, implementing the rulings of a non-Muslim judiciary is an acceptable matter, as it falls under the bringing about of what is considered to be of interest and to deter what is considered to be of harm and may cause chaos, as stipulated by more than one of the most prominent Islamic scholars, such as Al-Izz ibn Abdul Salam, Ibn Taymiyyah and Al-Shatibi.