I'll take it as a given that the readers are all familiar with the agreement that was struck between an Israeli government committee and representatives of Reform and Conservative Judaism for a mixed prayer area at the Western Wall only for the agreement to be nixed when chareidi parties threatened to bring down the government if it went into effect. Without getting into the merits of the deal, why are the chareidim so opposed to the deal? Would the area that would have been allocated for mixed prayer have in any way have reduced the ability of those who insist on separate-gender prayer space to pray at the Wall? Obviously this is not the case. The reason is that the chareidim view prayer at the Wall in a manner contrary to halacha as a defilement of the sacred space. They did not describe those who pray in mixed gatherings as trespassing "with their filthy feet," but the non-Orthodox Jews who thought they had an agreement would have justification to read that into them.
Similar to mixed prayer being restricted at the Wall, the Waqf goes apoplectic about Jews simply setting foot on the Temple Mount, let alone praying. This raises the question about why the Waqf, and the rest of the Palestinian national movement (PNM) is so against Jews at their most sacred site. No one can seriously claim that Jews walking around the site, even in substantially larger numbers than at present, impinges on Muslims praying at the Dome of the Rock or Al Aqsa. Same with Jews praying on the mountain. So why does the PNM oppose Jews' presence on the mountain so vehemently, referring that presence as defiling the site with their "filthy feet?" The simplest explanation is that Jews ascending and praying on the mount would remove one more manner in which they lord Islam's superiority of Judaism. The thing is that the preeners who notice and excoriate that behavior in the chareidi establishment regarding non-Orthodox Judaism will circle the wagons to assert that the Waqf has a legitimate interest in doing so with all Jews.