Firstly, the consensus among scholars is that a non-Muslim cannot act as a guardian (wali) for a Muslim. This is based on the Quranic verse: “And never will Allah give the disbelievers over the believers a way [to overcome them]” (Quran 4:141). Therefore, the Muslim woman should be married off by one of her Muslim relatives. If she does not have any Muslim relatives, then the ruler (sultan) becomes the guardian for someone who has no guardian, and the judge or the imam acts on his behalf.
Secondly, if the Muslim sister faces difficulty with her family regarding excluding her non-Muslim father from acting as her guardian, then it is better for her to initiate the marriage contract by herself. The marriage contract is valid according to the Hanafi School of law in the presence of her family members.
Fatwa by Dr. Khālid Naṣr