If a rav (or group of rabbanim) is convinced that another rav is involved in serious aveiros such as arayos and abuse, due to email evidence, multiple individual testimonies etc., and that he is a sakana to the tzibbur, or even that it is wholly inappropriate for him to serve as a rav, is it permitted for him (or them) to publicly announce his view, or must he (or they) respect the second rav’s demand that the matter be referred to an external beis din? Would it make a difference if the first rav (or group of rabbanim) was convinced that the second was merely using this as a stalling tactic?
The Takanah forum, which is made up of a number of members from the rabbinate and the public sphere of the Religious Zionist sector, is well known, and I understand the question refers to the activities of this forum or those of a similar theoretical forum.
The existence of such a forum is legitimate, but the yardstick for answering the question is the specific circumstances of each case.
If the circumstances are such that there is a danger to the public, and there is no efficient alternative for dealing with the threat, then publicizing the case will be permitted.
It is possible that the circumstancial evidence mentioned in the question will not be enough for punishments of Beis Din, but provided the evidence is conclusive it will be enough for taking the necessary measures for saving the community from damage (similar to the principles we find in Choshen Mishpat 2).
However, of course it will not be permitted to publicize the issue if the evidence is not conclusive, if the threat is not concrete, or if there is an alternative efficient means of dealing with the problem. If an external Beis Din is possible as a way of dealing with the issue, this must means of action must first be exhausted.
In addition, care must be taken to minimize the Chilul Hashem that can result from publication of the matter, and the entire matter must be done after consultation with Gedolei Yisrael.
The person in question must also be warned before the action is taken – all in accordance with the particular circumstances of the case.