For many years it has been the custom of Rabbi Dr. Moshe Dovid Tendler, famed posek, professor, and son-in-law of the great Rabbi Moshe Feinstein, זצ’ל to perform the commandment of “Mora Mikdash” – showing reverence to G-d at the place of the Holy Temple, by ascending the Temple Mount in strict accordance with halacha – Jewish law.
The Rabbi ascends the Mount every time he is in the land of Israel. He has made tens of visits to the Temple Mount.
This is the link of Rabbi Moshe Kurtz’s eulogy of Rabbi Tendler: https://www.yutorah.org/sidebar/lecture.cfm/1012783/rabbi-moshe-kurtz/my-chavrusa-rav-tendler-reflections-on-learning-directly-with-r-dr-moshe-dovid-tendler-zt-l/
Comment: There is an interesting insight on why Rabbi Feinstein did not drink non-Chalav Yisrael milk in the talk even though he permitted it in the U.S.A. for others.
Comment 2: Ascent to the Temple Mount is a controversial issue. It is more common to find Rabbis in the Religious-Zionist camp that agree with Rabbi Tendler’s opinion and less common to find “Chareidi” rabbis who agree. Without stating an opinion, who is right and who is wrong, it should be pointed out that if you do follow Rabbi Tendler’s opinion on ascent to the Temple Mount, you should get instructions how to do it, without violating ritual purity laws and the commandment of “Mora Mikdash”. Rabbi Yehuda Levi who promotes ascent to the Temple Mount has provided an email for those seeking instruction on this issue Rabbiylevi@gmail.com