So why is it that the Herem [חרם excommunication] of the Gra is ignored? [That is his signature on the letter of excommunication.] I think it is because people do not realize that a herem is a regular halacha (law) based on nedarim נדרים (vows). The only question would be if a herem is made by someone qualified. Clearly he was qualified. So it applies according to the strict law.
[Why do I say it comes from nedarim (vows). That is because I saw this in the commentaries on Laws of Shavuot and Nedarim.
So what is a neder (vow)? It is when someone says, "This loaf of bread is forbidden to you like a karban."(קרבן sacrifice brought in the Temple) If that loaf belongs to the speaker, then the neder [vow] is valid, and the other person can not eat from that loaf. אדם יכול לאסור את שלו. So in the case of the Gra, the herem was valid, and anyone transgressing it even until today transgresses a prohibition of the Torah.
Rav Nahman I believe was a great tzadik and not under the herem. However he does not seem to have been aware of its validity. So while `I think the best idea is to be part of a straight Litvak yeshiva, I can see the importance of following the advice of Rav Nahman in the many areas that he touches on. [Rav Nahman himself said a prophet knows only what is revealed to him. He is not "all knowing". It is a mistake to think of any tzadik as impervious to mistake--even the greatest like Moses as we see in the Torah in the case of the waters of Meriva
SO in short there are two reasons to be careful about the herem of the Gra. One: it matters not if one agrees with it. It still has halachic validity. Two: is refers to objective reality.
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