How does a woman perform ablution for Hajj, including washing hands and wiping the head and feet, in the presence of non-mahram men?

If a woman needs to purify herself in the presence of non-mahram men, she must cover herself or ask them to leave, then perform purification. If she is unable to do so, she should perform tayammum and pray, and it is not permissible for her to expose her awrah in front of them.

However, if a man is among men or a woman is among women, the Hanafis are of the view that ghusl is obligatory and is not waived for the sake of exposing the awrah. Yet, they held that a woman among men or a man among women should perform tayammum because exposing the awrah is not permissible. The commentator of Munyat al-Musalli among the Hanafis disagreed with them, and the statements of the Hanbalis also indicate disagreement with the Hanafis.

The Malikis and Shafiis are of the view that if performing water purification necessitates exposing the awrah, then one should resort to tayammum, because covering the awrah has no substitute, whereas water purification has a substitute.