Have famous rabbis ever converted to Islam?

No. If conversion is contemplated, apostacy has occurred. The person is no longer a Rabbi though he may have previously been awarded that title.

A Rabbi is one who has received semikah, ordination, to teach and judge in a stipulated manner. He is entitled to certain special forms of compensation and a higher degree of protection and respect so long as he discharges Rabbinical functions. However, except under extreme and sudden duress or as a result of insanity, it can't be the case that a Rabbi remained a Rabbi at a time when he converted to another Religion. So, technically, an apostate converts, a Rabbi doesn't- save due to sudden insanity or extreme torture or the threat of death.

On the other hand, it is certainly true that there have been periods when it was not clear whether apostacy had actually occurred. Perhaps Islam was complementary to Judaism? That doubt has been resolved. On the other hand, suppose your Rabbi is doing Yoga or Tai Chi. Does that represent a dangerous embrace of an alien, perhaps idolatrous, religion (avodah zarah)? In the case of Yoga, this matter has been resolved in Israel such that some aspects of it are kosher while others are not. This is a matter which required detailed inquiry and examination. Similarly, if a person who has the title of Rabbi and whose religious judgments have been followed, suddenly converts to Islam, there would have to be a proper examination to see whether or not he was truly discharging Rabbinical functions in the stipulated manner at the time when he began contemplating conversion. It is likely that he did something which caused him to become an apostate before the moment of conversion. If such is not the case, then the question arises- 'should Jews follow the example of this Rabbi? Should they too convert?' Clearly, accepting that a convert is a Rabbi at the time of conversion means accepting that the Holy Covenant is mutable. This must be rejected or else schisms will flourish and the Religion will decline.

On the other hand, it is certainly true that there are numerous communities across the globe who claim to have Jewish heritage. Some mention a particular Rabbi as having founded their lineage. There are instances where the two Chief Rabbis of Israel have investigated such claims with a view to determine if such people qualify for Aliyah under the 'right to return'. It would be interesting to find out whether, in granting such rights, Israel has tacitly admitted that Rabbis could convert while remaining Rabbis.

The 17th century Sephardic cult leader and kabbalist Sabbatai Zevi might be considered an example, though his conversion was coerced.

He claimed to be the Jewish Messiah and was invited by his Ottoman captors to choose between putting this to a probably fatal test, or converting to Islam.

Yes

Following are some examples of leading Rabbis who converted to Islam:

• Abdullah Bin Salam: He is the first Jewish Rabbi to convert to Islam. Before conversion he was called as Husayn bun Salam. The conversion happened at the time of Muhammad himself. Following narrative about his conversion is reported in the collection of authentic historical traditions of Islam:

Prophet Muhammad asks the Jewish community:

“What is the status of Al-Husayn ibn Salam among you?”

“He is our sayyid (leader) and the son of our sayyid. He is our rabbi and our alim (scholar), the son of our rabbi and alim.”

“If you come to know that he has accepted Islam, would you accept Islam also?” asked the Prophet.

“God forbid! He would not accept Islam. May God protect him from accepting Islam,” they said, horrified.

At this point I came out in full view of them and announced: “O assembly of Jews! Be conscious of God and accept what Muhammad has brought. By God, you certainly know that he is the Messenger of God and you can find prophecies about him and mention of his name and characteristics in your Torah. I for my part declare that he is the Messenger of God. I have faith in him and believe that he is true. I know him.”

• Sabatai Zevi : Was a very famous Rabbi of his time , to the extent many of the Jews started believing him as the Messiah and he claimed it too. Some people claim that he was coerced , this might be true but later in life he truly accepted Islam and also bought 300 Jewish families to Islam:

Sarah and approximately 300 families among Sabbatai's followers also converted to Islam. These new Muslims thereafter were known as dönmeh (converts).3 The sultan's officials ordered Sabbatai to take an additional wife to demonstrate his conversion. Some days after his conversion he wrote to Smyrna: "God has made me an Ishmaelite; He commanded, and it was done. The ninth day of my regeneration."

• Maimonides - (RAMBAM) : Many historical sources seem to support the idea that RAMBAM may have been coerced into converting to Islam, although this is highly debatable:

Some references:

A Muslim historian, Ibn al-Qifti (1172-1248) reports nothing less than that the Rambam himself, on numerous occasions, voluntarily went to mosques to pray 1, under no compulsion and seeing no contradiction with his Judaism. Ibn al-Qifti notes that this was towards the end of Maimonides’ life and was not an event of his youth, under fear of the Al-Mohades who had invaded Al-Andalus in his youth.1

Kenneth Seeskin writes, in The Cambridge Companion to Maimonides, “although Ibn al-Qifti’s book has come down to us in a later recension, and contains some errors, we have no reason to doubt the information on Maimonides.”2

1 Tarikh al-Hukama, p. 318, trans. Kraemer in Fine, 2001. 424.

2 Kenneth Seeskin, The Cambridge Companion to Maimonides, (Cambridge University Press: 2005)

Moreover many of the famous works of Maimonides are derivatives of the Islamic literature by Muslim scholars. The Rabbis of the time of Maimonides condemned RamBam for bringing Islamic scholarship into Judaism. Later down the line his grandson Obadyah (1228-1265) accepted and followed the mystical notions of the Muslim Sufis and wrote the classical treatise on Islamic sufism interlaced with Jewish thoughts titled as The Treatise of the Pool: Al-Mawala Al Hawdiyya.

A UNESCO historical document states the following on Pg 14:

Some biographers maintain that Maimonides may even have been converted to Islam.

Also, in the French version of a December 2010 report of UNESCO we find the following report:

Une fois Tolède reprise aux Maures par les croisés en 1085, les savants européens y affluèrent afin de traduire les anciens textes classiques du grec (que l’Europe avait oubliés) vers l’arabe et l’hébreu, puis le latin, rendant ce la première partie du Moyen Âge européen (1100-1543), les noms de quelques savants européens apparaissaient dans la littérature scientifique à côté d’un grand nombre de savants musulmans, parmi lesquels Ibn Rushd (Averroès), Moussa ibn Maïmoun (Maïmonide), Tousi et Ibn Nafis.

After the recovery of Toledo from the Moors by the Crusaders in 1085, European scholars flocked there to translate the ancient classical texts from the Greek (which Europe had forgotten) to Arabic and Hebrew and Latin, making it the first part of the European Middle Ages (1100-1543), the names of some European scholars appeared in scientific literature next to a large number of Muslim scholars, including Ibn Rushd (Averroes), Maimouna Ibn Moussa (Maimonides), Tousi and Ibn Nafis.

Having said that, although RAMBAM may have at some point feigned conversion because of social and political pressure, it does not appear that was truly a believer in Islam. See Historian reviews evidence of Rambam’s forced conversion

Another point of view regarding Rambam can be that he practiced both Judaism and Islam simultaneously, In Jewish Encyclopedia , we find the fact that , belief in Muhammad pbuh is not equatable to Idolatry and hence wont demand sacrifice of life as is the case of the law for Idolatry, thus making Islam simply as a sect within Judaism:

Rabbi M. Friedländer in ("Guide of the Perplexed," i., xvii., xxxiii., et seq.), in which Islam is declared to be simply a belief in Mohammed, and that Islam is not idolatry, to avoid which only the Law demands the sacrifice of life.

Jewish Encyclopedia

Hence it is halachically possible for a Jew to become a Muslim , A Jew wont loose his Jewishness by accepting Islam. Rambam realized this very well as quoted above in his most popular work. hence it is fair seeming that he purposely did not show any resistance to Dawah on him and accepted Islam. His acceptance of Islam may not be genuine but he was a very ambitious and rational intellectual whose conversion was a pragmatic decision which would help him gain acceptance and position of influence from the Sultans of the time as reported by Al-Baghdadi in Seeskin:

he was of superior merit, but love of authority and serving powerful people prevailed over him

was too much concerned with worldly successand frequenting the great as their physician

Reports from Kenneth Seeskin, The Cambridge Companion to Maimonides, (Cambridge University Press: 2005)

Regarding conversion:

Kraemer also found sources that indicate that while in Fustat (old Cairo), the Rambam was confronted by a man named Abu ‘l-’Arab ibn Mu’isha, a jurist from Andalusia, who recognized that the leader of the Jewish community in Egypt was no longer practicing Islam (a crime punishable by death under Islamic law). The Rambam managed to escape persecution although the historical records give conflicting reports as to how that happened.

• Moisha Krivitsky, Ex-Rabbi, Dagestan: He is reported to be the Rabbi of Makhachkala synagogue in Dagestan

• Abu Nasr Samuel ibn Judah ibn Abbas (Samuel of Morocco): He was the rabbi of the Moroccon city of Fez and author of the "IfḦam al-Yahud"(Confutation of the Jews) a polemical treatise written addressed to the Jews after conversion to Islam. The Jewish encyclopedia summarizes his work:

In this work (Ifham Yahud) he points out that from time to time the abrogation of the Law is necessary and that, in fact, it has often occurred in Judaism. He tries to prove the prophetic character of Jesus and of Mohammed; claiming that the first of these is referred to in Gen. xlix. 10, and the latter in Gen. xvii. 2 ( has numerically the same value as Mohammed). He affirms that the Jews of his time possess the Torah of Ezra and not that of Moses, and that too many laws have been added by the sages of the Mishnah and the Gemara.

Samuel makes the curious statement in ("Monatsschrift," xlii. 260) :

that most of the Karaites had gone over to Islam, because their system is free from all the absurdities of the Rabbinites, and their theology not so different from that of the Mohammedans.

• Yosef Cohen A former rabbi belonging to the Satmar Hasidic community in Brooklyn.