There are certain sections of the Temple mount where Jews are halachically forbidden from going, namely the area where the Kedush Kedushin (Holy of Holies). However if a secular Jew who does not follow halacha wants to go up with a group on another 9 Jews, they are not allowed. The main reason is that the Israeli authorities are pretrified that the arabs will riot. Shows you how tolerant the arabs are.
In three days, Greek coastguard rescues 2,500 migrants (Reuters)
from the article: Israel must allow Palestinians to protest in peace