How can one respond to those who permit mixing, citing that the forbidden mixing is only that which involves touching or proximity that incites desire, and that the verse of Hijab is specific to the Mothers of the Believers, and that mixing exists in the Grand Mosque of Mecca, and that there was no barrier between men and women during the time of the Prophet, peace be upon him?

The gathering of men and women under one roof is not inherently forbidden. This is evidenced by the prayer of men and women together in the mosque of the Prophet, peace and blessings be upon him. The claim that the verse of hijab, "And when you ask them [his wives] for anything, ask them from behind a partition," is exclusive to the wives of the Prophet, peace and blessings be upon him, is incorrect. This is because Allah obligated hijab upon the purest of women due to their purity, and the ruling is based on the generality of the wording, not on the specificity of the cause. Furthermore, an address to the Prophet, peace and blessings be upon him, includes the entire Ummah unless there is evidence that specifies otherwise. The reliance of some on the permissibility of intermingling in the Haram (Grand Mosque) as proof of its permissibility elsewhere is incorrect; intermingling in the Haram is due to the high population density in a confined area for the performance of a specific act of worship. Therefore, the widespread intermingling seen in universities and other places today is not permissible.