Temple denial is the claim that the successive Temples in Jerusalem either did not exist or they did exist but they were not constructed on the site of the Temple Mount

https://en.wikipedia.org/wiki/Temple_denial

The wailing wall is not part of temple mount

https://web.archive.org/web/20170928202735/https://theolivetdiscourse.com/the-wailing-wall-is-not-part-of-temple-mount/

https://web.archive.org/web/20190830074821/https://i1.wp.com/theolivetdiscourse.com/wp-content/uploads/2017/04/Temple-Mount-fs-1.gif

If the wailing wall is not part of the temple than they could rebuild the temple while also letting Muslims use the dome of the rock

They could have segregated worship services without conflict