Cohanim and Kivrei Tzaddikim (the graves of the righteous)

Our Rabbi told the following story about Maran Ha-Rav Kook (Le-Shelosha Ba-Elul vol.1 #76), that during his travels to oversee Jewish matters in the Galil, he did not visit Kivrei Tzadkim when he was in Tzefat, because he was a Cohain.

Ha-Rav Mordechai Eliyahu wrote (Parashah Sheet "Kol Tzofa’ich #279), "In his time, I told Ha-Rav Ha-Gaon Tzvi Yehudah Ha-Cohain Kook, peace be upon him, that it is written in the book ‘Kuntres Yechi’eli’ that it is permissible for cohanim to enter Kever Rachel. He asked me: what do they say there? I said that they read the verses about our mother Rachel there. He travelled there, but only went as far as the door. When he returned, I asked him: why didn’t you enter? He answered: My father did not enter, therefore I did not enter."

In the book Sichot Ha-Rav Tzvi Yehudah - Eretz Yisrael (edited by Rav Shlomo Aviner, p. 142 note 1), it relates that after the Six-Day War, the students of our Rabbi organized a trip to the liberated areas in the Shomron. One of the places they visted was Kever Yosef. The students entered inside, but our Rabbi remained outside, because he was a cohain.
And on Maran Ha-Rav Kook's yahrtzeit, our Rabbi, Ha-Rav Tzvi Yehudah, would visit his grave on the Mt. of Olives, but would stand at a distance since he was a cohain (Be-Derech Ha-Torah Ha-Goelet, p. 170).

In Iturei Cohanim (Sivan 5766 #261), Rav Aviner was asked, is it permissible for a cohain to enter Ma’arat Ha-Machpelah? He answered that there is a dispute, but Maran Ha-Rav Kook did not enter. Similarly, in the weekly parashah sheet "Olam Katan" (#169), Rav Aviner was asked, is it permissible for a cohain to enter Ma’arat Ha-Machpelah to recite Selichot? He answered that there is a dispute, but Maran Ha-Rav Kook did not enter. In Shut She’eilat Shlomo (vol. 3 #329), Rav Aviner also writes that although there are authorities who permit cohanim to enter "Kivrei Tzaddikim," since the righteous are called "living even in their death," the accepted halachah is that it is forbidden. There are also authorities who allow cohanim to visit Maarat Ha-Machpelah and Kever Rachel, because they were built in a way that the cohanim would not become impure; but the acceptable halachah for this is also that it is forbidden. Therefore, we say that cohanim should not enter "Kivrei Tzaddikim," but we can defend the practice of those who act in this way, especially entering Maarat Ha-Machpelah and Kever Rachel.

In the book "Ke-Chitzim Be-Yad Giborim" (vol. 3, p. 108), Ha-Rav Avi Ronski, the current Chief Rabbi of Tzahal, was asked: is it permissible for a soldier who is a cohain to enter Ma'arat Ha-Machpelah for a tour in order to learn about the place in the event of a terrorist attack and his unit is required to take action? Rav Ronski answers that it is permissible for three reasons: 1. It is obvious and clear that the security apparatus that would be sent on such a mission must train for it properly. 2. In general, it is not clear that the graves of our forefathers are directly located under the floor of the prayer halls, and even if they are located there, it is possible that the impurity does not break out and spread upward since it is possible that there are hollow spaces larger than a "tefach" (handbreath – 7.6 cm-9.6 cm) which separate between the floor and the graves. 3. There are Rishonim (Rabbis of the Middle Ages) who ruled that the graves of the righteous do not cause impurity, and Ha-Rav Mordechai Eliyahu permits cohanim to enter Ma'arat Ha-Machpelah and Kever Rachel. Even though the majority of authorities prohibit entering, it is possible to add this lenient opinion to the other reasons to permit it. Rav Aviner writes in his comments to this book that it is important to know that the first reason is the main one, and the second and third reasons are only additional minority positions which can be added to permit it. And we must point this out so that people do not learn that there is a blanket permission to enter.

Note: Rav Aviner – who is also a cohain – has not and does not visit any of the "Kivrei Tzaddikim."