Can my wife remove here Hijab in front of here step-father? Please note that my mother in-law is not a Muslim nor is her husband.
Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
The woman is allowed to remove her Hijab in front of the husband of her mother as he is considered a Mahram for her. This rule applies to the Muslim and non-Muslim step-father as there is no difference as far as the rules of Mahram between a Muslim and a non-Muslim is concerned. So, the woman is allowed to shake hands, stay alone and travel with her step-father whether is he a Muslim or a non-Muslim unless he is known to be one of the people who make it lawful to have sex with one's Maharim or to be a cuckold who does not have any jealousy over his household, in this case, he is considered a foreigner and must be dealt with accordingly. The evidence that the step-father is Mahram to the step-daughter is the following verse: Allah Says (interpretation of meaning): {…, your step daughters under your guardianship, born of your wives to whom you have gone in - } [4: 23].
Allah knows best.
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