The practical ruling of Gedolei Yisrael:
In both the previous and current generation, the Poskim and Gedolei Yisrael from all spectrums of Jewry, have severely warned the public not to enter the Temple Mount, including even the permitted unrestricted areas, lest he enter a restricted area and be liable for the severe penalty of Kareis. Meaning, that even if we can determine without shadow of a doubt the exact areas of restriction, or of questionable restriction, and the areas that are permitted in entry according to all, nevertheless, one should not enter even these areas, as doing so would cause others who are unaware or not G-d fearing to enter the prohibited areas.
Security forces entering the Temple mount: It is permitted for security forces to enter the Temple Mount area, and even the Kodesh Hakedoshim, in order to prevent a life-threatening situation, such as to fight Arab terror which commonly occurs on the Temple Mount. Nonetheless, being that in many cases, the police send units up even during times that are free of danger, therefore a G-d fearing Jew is not to accept such a position. Commonly, due to this reason, there is a high percentage of non-Jewish soldiers who patrol the area, in order to avoid religious conflict.
Gedolei Yisrael from all spectrums of Jewry prohibit visitation to the Temple Mount, including to those areas which have been determined to not be part of the Halachic Har Habayis and are not restricted in entry.
The Rebbe’s approach:
In a letter to Rabbi Meir Yehuda Geitz, the chief Rabbi of the Kosel, the Rebbe stated as follows:
It is obvious that in the current state of affairs in which the public is waring from right to left [further away from Torah] that I am most vehemently against even the mere public discussion of the question of allowance to enter Har Habayis. [The reason for my absolute opposition is] because the moment that this discussion would begin, a number of people will visit the area, including the areas which are certainly prohibited, G-d save us, and that number will continue to grow, G-d have mercy on us. All the warnings about this issue (assuming they would be issued) will simply ignite the inclination of those people and increase the amount of people who go. Whoever brings up or participates in the discussion of this issue, and certainly one who actually goes up to Har Habayis, in addition to the sacrilege of the elders of Jerusalem, and the city of Jerusalem, it is sacrilege of the Har Habayis itself. Upashut!
 See Piskeiy Teshuvos 561/5
 Minchas Yitzchak 5/1; Yabia Omer 5/26; Tzitz Eliezer 10/1; Rav Elyashiv; Rav Wozner; Rav SZ”A; Rav Zevin; Rav Yaakov Landa; Rav Kook; Rav Mordechai Eliyahu; Rav Avinar; Chief Rabbi’s of Israel in their respective terms including Rav Kook
 Rebbe ibid
 Heard from Harav Yaakov Yosef
 Printed in Menachem Meishiv Nafshi Erech “Rav Geitz”