Ascending the Temple Mount nowadays

 Temple Mount Akeida 

Bereishis (22:2) And he said, Take now your son, your only son Isaac, whom you love, and go to the land of Moriah (Temple Mount); and offer him there for a burnt offering upon one of the mountains which I will tell you.

Ascending the Temple Mount nowadays 

Igros Moshe (OH II:113) Question Why the Tur and the Shulchan Aruch do not mention that it is prohibited to spit today on the Temple mount? Answer: Iit is irrelevant since it is prohibited for those who are impure from the dead  (as everyone today has that status) to go there. In fact, however, there are places on the Temple mount that it is permitted for those impure from the dead to enter even according to Rabbinic prohibition. That is until the Chayel which is before the Soreg.  The Rambam writes that the Soreg encloses and possibly the Chayel encloses as is explained by Tosfos Yom Tov. That would mean it would be permitted from all sides even on the west, for those who are spiritually impure to enter up to the Soreg which is a number of amos wide. I couldn’t find the exact measure.  However according to the Rosh the Soreg is only on the east  from north to south it is possible that the Chayel is only there, if so then on the other sides after 10 amos of the Chayel behind  the Ezras Nashim it would be permitted. Also on the western side it would be permitted for the impure from the dead as well as other impurities since they can go to mikveh. If you are concerned for zivah they can count seven clean days and then tovel in a mikveh and after the sun sets they would be spiritually pure. Even if they didn’t bring a korban, they are allowed in the Ezras Nashim and surely on the rest of the Temple Mount as stated by the Rambam. .In conclusion we find that regarding the prohibition of spitting on the Temple Mount, those places where it is prohibited to spit it is also prohibited for the impure from the dead to enter Perhaps the problem is that it is not so clear which wall. If there is a clear tradition that it is the Western Wall of the Temple Mount or the Wall of the Ezara behind the Kapores then it would definitely be prohibited for the impure from the dead.  It is also possible that it is the lower wall which is prohibited even according to the Rosh.  I seem to recall that Rav Dovid Karliner was uncertain which wall. Perhaps this is the reason that they say about the Brisker Rav that he did not go to the Western Wall because of concerns for spiritual impurity. But I find that astounding! The place that Jews have prayed for many generations, obviously has a tradition from the ancient rabbis that it is permitted to go there – so how can anyone disagree with them?