What is the ruling on the marriage of a veiled woman to an irreligious man?

A Muslim woman should not accept marriage except from one whose religious commitment and character are pleasing, because weakness in faith and lack of adherence to Islamic law lead to significant dysfunction within the family. There is variation among people in their religious commitment; a man might be righteous with some shortcomings, or his shortcomings might be destructive to the very foundation of religion, such as his affiliation with deviant ideologies, or his abandonment of prayer, or his addiction to alcohol. It is not permissible for a Muslim woman to marry one who abandons prayer, or is addicted to alcohol, or is an innovator (Mubtadi’), or belongs to a deviant materialistic ideology. It is advised to investigate the suitor’s religious commitment, character, and adherence to prayer and the mosque, and to know his family and friends. Money, lineage, or profession should not be a reason to overlook these aspects, as doing so may lead to the misery of the wife and her children.