I haven’t been to Israel in years, but when I did go, tourists were allowed on the Temple Mount, even into the Dome of the Rock. Only Jews were not allowed on the site.
Have the “rules” changed?
“Only Jews were not allowed on the site.” It’s because that that area has not been “sanctified(see Red Heifer)” since the “Abomination of Desolation(70AD-Titus-Roman Army)”. When it is then the Temple will be re-built.
http://www.frommers.com/destinations/jerusalem/0088032100.html
...Although visitors may walk around on the Temple Mount, take photographs, and enjoy the vistas, for now entry into the Dome of the Rock, the Al Aqsa Mosque, and the Islamic Museum is not permitted. Longer visiting hours and permission to enter the buildings on the Temple Mount may be restored during the time span of this edition. The Temple Mount is always closed to non-Muslims on Friday and during the entire holy month of Ramadan.