Even before his death, Rabbi Shlomo Carlebach was, at best, controversial. Many people loved his music and some congregations organized "Carlebach minyans" that emphasized spirituality through music. But my rav, Rabbi Gedaliah Anemer, refused to allow any minyan to refer to Carlebach. Another rav, Rabbi Rod Glowgower told me 25 years ago, that he was reluctant to grant shul membership to a female convert of "Reb Shlomo." And Rav Moshe Feinstein reportedly wrote an opinion critical of him. Since his death, women have come out with explicit reports that Carlebach was a sexual predator. See this and this. In light of the public allegations, have there been any bans on his music or rabbinic acts such as conversions?
Bruce, may you live and be well to 120, but I'm reminded here of someone's definition of a "Jewish question": someone gets up and makes a big statement, then just raises the pitch at the very end so it sounds like a question.
I don't know what you mean by "predator", I don't know what the allegations are, I don't care. Let's talk theory here. Rabbi Moshe Feinstein described a certain individual, and sets out the following concepts:
If someone actively rejected the basic tenets of Orthodox Judaism (or publicly violated the Sabbath while staring the rabbi in the eye, or worshipped idols), then we would invalidate a Torah scroll he wrote. Rabbi Feinstein says this is limited to the realm of religious objects. We are perfectly allowed to use -- and refer to by name -- Von Neumann computer architecture, or the Salk vaccine, or the like; regardless of how much of Judaism John Von Neumann or Jonas Salk knew or kept. (Concept is Feinstein, examples are mine.) Rabbi Feinstein writes that the music played at Jewish weddings is not an inherrently ritual object, hence it's merely inadvisable, not prohibited, to play music composed by a heretic at a Jewish wedding.
If, however, an individual in theory believes in everything, but succumbs to various vices, then in other aspects of halacha they are not invalidated. The subject of Rabbi Feinstein's responsum falls under this category, hence his music is perfectly permissible at weddings, even for the very pious.
From reading this I would gather that new allegations would not "invalidate" the music.
Now if we believe that an individual truly victimized many people and by acknowledging him we will cause anguish to the victims, or give our community a black eye as it appears we condone horrible behavior, then that's a question of between-man-and-fellow-man. You'd have to know the particulars of the case. I know of a synagogue with a retired rabbi who was later convicted of serious offenses; the synagogue struggled with whether to remove every trace of his name from every letterhead and plaque. These are tough questions, but they're matters of nuance. There's no open-and-shut mishnah brurah on this.
As for conversions performed, again one would have to know the particulars of each case performed. The Talmud describes how a man served as High Priest of the Temple for decades and decades before leaving the path of mainstream Judaism. Humans are complicated; if G-d wanted simple, reliable creatures, He had plenty of angels! If a rabbi on the panel had rejected Orthodox theology at the time of the conversion, that's one story. If he struggled with personal demons, that's not so simple. Rabbi Hershel Schachter recalls hearing of Jewish couple who sought to retroactively dissolve their marriage, rather than divorce, so she could marry a Cohen. The argument was that one of the rabbis witnessing their wedding later checked into rehab for sex addiction and had been seeing women-of-ill-repute on a regular basis. (G-d have mercy!) Besides other, more-gaping holes in their argument, Rabbi Schachter wasn't sure if that would be enough to invalidate the ceremony. (Though the bar is higher for "rabbinic judges" than for witnesses.)
As for adopting someone's teachings, well Rambam says we accept truth from wherever its source. If someone tells me "Pizza Yehopitz is the tastiest pie in town" (let's assume the kashrut is unquestioned), I'm welcome to try it regardless of that fellow's morals. Certainly one should weigh the totality of a person's teachings and deeds before adopting all their teachings as a raisson d'etre, but that should be nothing new.