Praise be to Allah.
The scholars (may Allaah have mercy on them) mentioned the conditions for being a woman’s wali (guardian) for marriage. Some of these conditions are agreed upon, and others are disputed. The conditions that are agreed upon are:
Ibn Quddamah said: The kaafir cannot be the wali of a Muslim woman, according to the consensus of the scholars.
A similar view was also narrated from Ibn al-Mundhir. (al-Mughni, 7/356)
2.Being of sound mind.
3.Majority (having reached puberty)
Ibn Rushd said: (The scholars) agreed that among the conditions of guardianship are: being Muslim, being an adult and being male.
Bidaayat al-Mujtahid, 2/12
Ibn Qudaamah said: Being male is a condition of guardianship according to all (the scholars). (al-Mughni, 7/356)
The conditions concerning which the scholars disputed are:
The condition of being free is listed by most of the scholars; the Hanafis were of a different view.
The basis of describing freedom as a condition is that a slave has no power of guardianship over himself, so it is more likely that he cannot have the power of guardianship over anyone else.
(See the two references mentioned above)
2.Being of good character
Imaam al-Shaafa'i and Imaam Ahmad were of the view that this is one of the conditions of guardianship.
What is meant by good character is appearing to be of good character. It is not necessary for the wali to be of good character both outwardly and inwardly. Such a requirement would be too difficult and would lead to most marriages being invalid. (Khashshaaf al-Qinaa’, 3/30)
It is important to note that the questioner may want to marry the woman, then if he discusses some issues with her guardian and they have an argument, he might accuse him of not believing in referring to the Qur’aan and Sunnah. This would be overstepping the mark and a major sin, because it is accusing a Muslim of something that would put him beyond the pale of Islam.
But if the wife’s guardian really does not believe in the Sunnah, like that group which calls itself al-Qur’aaniyyeen, then he should argue with him, explain the truth to him, dispel his confusion and establish proof against him. Then if he persists he is a kaafir, and it is not permissible for him to be the guardian of a Muslim woman for marriage even if she is his daughter. He forfeits the right of guardianship, which then passes to the closest Muslim relative of the woman. And Allah knows best.