I was directed to this on yeshivaworld.com
HaRav Shlomo HaKohen Aviner Shlita was asked about Jews visiting Har Habayis. The rav explained there are rabbonim who permit it under certain conditions while others do not, adding those who do not are gedolei hador and even among rabbonim one must realize there are differences. He added the Chief Rabbinate of Israel opposes it and that is what defines the issue.
Rav Aviner adds that when HaGaon HaRav Hershel Schachter of Yeshiva University was asked, he explained as a rav in the United States he will not responsd but pointed out the Chief Rabbinate of Israel prohibits it. “Neturei Karta and Agudas Yisrael do not listen to the Chief Rabbinate, just the dati’im - the nationalists and if we do not do as instructed, this will lead to the collapse of the Chief Rabbinate of Israel”. Rav Aviner explains that HaGaon HaRav Moshe Feinstein ZT”L teaches us that one rav cannot give a psak for another, “and the Rav from Minsk does not become involved in matters pertaining to the Rav of Pinsk”.
The chareidi rabbonim do not speak about the prohibition of visiting Har Habayis because it is understood. “Once when someone asked HaGaon HaRav Elyashiv ZT”L about going to Har Habayis he responded ‘chas v’sholom’ and the gabbai responded ‘you ask such questions to the rav, dealing with kores’. Rav Elyashiv responded ‘even if there isn’t kores, לא יטמאו את מחניהם אשר אני שוכן בתוכם”.
Rav Aviner continues, explaining shortly after Har Habayis was liberated the Steipler ZT”L published a notice citing the severity of violating the prohibition regarding Har Habayis. Rav Aviner adds that the Steipler’s talmidim gathered the signatures of leading chareidi poskim. as it was about to be printed it went to the Chief Rabbinate and then they said the printing was no longer necessary since the prohibition was already issued. (אורחות רבנו א שכד-שכח).
Hence concludes Rav Aviner, visiting Har Habayis is an affront to both the Chief Rabbinate of Israel and Gedolei Yisrael. The rav concludes that visiting Har Habayis results in blurring the various levels, adding Rav Tzvi Yehuda Kook taught about preserving and maintain the “binyan shalem” created by HKBH; Am Yisrael and Eretz Yisrael, all levels. “There is a life-threatening danger when the various areas are blurred, blurring the levels of kedusha. When Miriam compared the level of Moshe to the other prophets it was a burring of levels and an avreira of comparing smaller to the larger”.