Is it permissible to adopt the view that the moisture of a woman's private parts does not nullify wudu', always, or in urgent cases such as during rituals in the Sacred Mosque in Mecca or Medina?

It is not permissible to say that vaginal discharges do not nullify ablution. The more cautious opinion is that they do nullify ablution. If they are continuous, then their ruling is similar to that of urinary incontinence. In this case, the woman purifies herself for the obligatory prayer after its time has begun, takes precautions as much as she can, and then prays. What is discharged thereafter does not harm her. However, if the discharge stops at a specific time before the prayer time ends, she must wait until the time when it ceases. If performing ablution for every prayer is difficult for someone with continuous discharge, then there is latitude in adopting the view of the Malikis. If the discharge stops for a period that is sufficient for purification and prayer, then she must pray within that time. Purification is not obligatory for the ritual walking (Sa'i) in Umrah; it is only obligatory for the circumambulation (Tawaf).