Every time the suggestion of introducing Islamic law in Western legal system is mentioned, it is tempered by its proponents with the sentence: this would only affect the family law. Ye it is precisely because this suggestion concerns family law, it should be rejected. For the issue here relates to nothing but legally sanctioned discrimination against women and children.
The system has furthermore been instrumental in the Islamization of societies where other religious minorities live. Simply put, the supremacy of Islamic law in cases of conflict, inheritance and guardianship has led to incremental effects that gradually led to the conversion of non-Muslims.
For example, the prohibition of mixed marriage between a Muslim woman and a non-Muslim man has a political function that makes sure that only Muslim men are allowed to marry non-Muslim women and so their children will automatically become part of the Muslim community. Non-Muslim women, however, are not allowed by law to inherit from their Muslim husbands unless they convert to Islam! Many will do exactly that for obvious reasons.
Read the whole article here.