The beliefs of a rabbi are no small issue. They can impact the validity of geirus, gittin and kiddushin performed under the rabbi’s review or that hinge upon his testimony, and the halachic integrity of those institutions that affiliate with a rabbi whose beliefs are unacceptable becomes suspect.
In other words, not only would any conversions, divorces or marriages performed by Rav Farber be invalid, but by association, any of those performed by anyone affiliated with YCT (Yeshivat Chovevei Torah - Rabbi Farber's alma mater) would also be invalid. I find this claim very disturbing.
Firstly, and obviously, I don't know why a marriage would be invalid, even if performed by a heretic. One does not require a Rabbi to perform a wedding.
But aside from that, to invalidate an entire institution based on the writings or thought of one individual sounds like a very dangerous precedent (not to mention that YCT have distanced themselves from Rabbi Farber's views, and stated openly that his views do not represent those of the school).
The kinds of sins which invalidate dayanim are (according to Shulchan Aruch) those that invalidate witnesses.
In Choshen Mishpat, siman 32 se'if 22 it states:
המוסרים לאנסים, והאפיקורסים והמומרים לעבודת כוכבים, פחותים מהעובדי כוכבים ופסולים לעדות.
those who hand over [Jews] to the secular authorities, and apikorsim (heretics) and those who are known to worship idols, are less valid than idolators, and are invalid as witnesses.
If it were to be decided that Rav Farber was an apikoros, he would be invalid as a judge (and witness) based on this halacha.
But if we look earlier in the siman, and the much longer discussion of other kinds of sins which invalidate judges (and witnesses) we find:
גנב, וכן גזלן, פסולים לעדות מעת שגנב או גזל, ואע"פ שהחזירו, עד שיעשו תשובה.
A thief or a robber are invalide for testimony from the moment they stole or robbed. Even if they return [the money they are still invalide] until they repent
Imagine, hypothetically, that a chief Rabbi of Israel would be indicted for fraud, bribery, money laundering and theft. If he were to be convicted, would that invalidate not only any beit din that he personally had sat on, but also every beit din under his jurisdiction? Were he to be found guilty, even if he repaid the money, would every divorce performed in Israel for the past several years be invalid? And how about every conversion? It would undermine the very fabric of society. (I'm not accusing anyone, nor do I think that anyone is guilty. This is a hypothetical question based on Rabbi Gordimer's assumption that any Beit Din associated with an individual Rabbi should be tarred with the same brush as an individual. This case would be worse, because the accused is the head of the organisation).
Or, Rambam writes in Hilchot Eidut, chapter 17 halacha 1
יז,א מי שהעידו לו אנשים רבים וגדולים בחכמה וביראה, שהם ראו פלוני שעבר עבירה פלונית, או שלווה מפלוני--אף על פי שהוא מאמין הדבר בליבו כאילו ראהו--לא יעיד, עד שיראה הדבר בעיניו, או יודה לו הלווה מפיו ויאמר לו, היה עליי עד: שנאמר "או ראה או ידע" (ויקרא ה,א). ואין לך עדות שמתקיימת בראייה או בידיעה, אלא עדות ממון. וכל המעיד מפי אחרים--הרי זה עד שקר, ועובר בלא תעשה: שנאמר "לא תענה בריעך עד שקר" (שמות כ,יב).
Someone to whom many people who are great in wisdom and fear of G-d, have testified that they saw someone transgress a sin... may not testify unless he sees it with his own eyes... Anyone who testifies based on the testimony of others is a false witness and transgresses the negative prohibition of "do not bear false witness agsinst your neighbour
Now imagine, hypothetically, that the head of a very large Rabbinic organisation in America was defending a convicted criminal based on evidence he had heard from others, and his own 'investigation' (this is not exactly the same as Rambam's halacha but pretty similar). Imagine if the Rabbi continued to insist on his innocence even after the criminal had confessed and pled guilty and been sentenced to jail. Furthermore, this Rabbi accused someone else of perpetrating the crime, with no evidence. And he continued to insist that he is correct and refused to retract either his claim of innocence on the confessed perpetrator, nor his unfounded allegations against an innocent party. (I am not saying that this is what happened - I have no evidence apart from what I've read and heard from others, but I am suggesting a hypothetical case).
Would Rabbi Gordimer then invalidate any gittin or geirus done under the auspices of this organisation?
These are two hypothetical examples that come to mind. There are (unfortunately) many cases of financial crimes, or other sins which would brand someone a 'rasha' which have been perpetrated by Rabbis and Dayanim. If we were to follow Rabbi Gordimer's lead and invalidate any action performed by any Beit Din associated with them it would be extremely difficult to find any Beit Din in the world that is kosher.
To repeat: I am not accusing anyone of guilt (or innocence). I do not know whether Rabbi Farber is a heretic or not (nor is my opinion relevant). And I do not know whether Rabbi Farber actually sits on a Beit Din or not, and what the status of that Beit Din will be in the future. I am simply pointing out that if Rabbi Gordimer is correct (and I haven't claimed that he is wrong) we will need to review the entire system of Beit Din within every Jewish community and every country, to ensure it meets the rigorous (minimum) standards of not being in any way associated with anyone who is invalid as a judge or witness. Not that is a tall order!