I was on the Temple Mount during a tour of Israel about two years ago. The Muslims have been permitted to manage the holiest site in Judaism. We were allowed access with permission from the Muslims when no prayers were going on, and we were not permitted to take any religious items, such as prayer shawls. We were told to be careful of what we said, and to not get caught saying any prayers, unless they were Islamic prayers.
The Muslims got caught excavating under the Temple Mount to build another mosque, without permission. When they got caught, they lied about it, and then took everything that they dug up, 2,000 plus years of archeological evidence of Jewish and Christian presence, smashed it to smithereens, and dumped it in a valley.
My wife and I were there during the Naqba protests going on (and Harold Camping had predicted the end of the world), and we did not get to the Temple Mount. Did the Wall and the Tunnel, but things were a bit tense at the time, so there were a few days it was recommended we not go into the Old City.
nothing quite like the Israeli jets flying over us as we were atop Masada.