We do spread the word, but we do not solicit converts.
Judaism is understandably primarily for Jews, but there is a component of law for the rest of the world. The fact that there are such laws, the "Noachide" laws, indicates quite clearly that we accept the reality of other religions.
There is no law in Judaism that we must change non-Jews into Jews, and there is no rule that only Jews have a share in the world to come. Quite the opposite - righteous non-Jews have a share in the world to come.
This is quite remarkable, that a religion, Judaism, affirms that members of other faiths are not disqualified from eternal bliss simply because they are non-Jewish. Other major reeligions are obliged to missionize, to save the non-members from the hell that awaits them for belonging to the wrong religion.
It is our appreciation of others that explains why we do not try to change others. As long as they are righteous, they are fine. And the message of righteousness we do spread, but not in a partisan manner.
Another matter to contemplate is that non-Jews are not obliged to eat kosher, for example. Should we "twist their arm" and get them to join, however reluctantly, then if they eat non-kosher food, they will be transgressing. In other words, getting them to agree to embrace a faith and its obligations when they really do not want and will probably not fulfill, is doing them a dis-service. We do them no favors by causing them to sin.
The important matter to realize in all this is that our reluctance to missionize is not because we do not want outsiders. It is because we value them as they are.
If you look at Judaic history, you will find that Judaism actually tried to make Judaism more spiritually appealing to the non-Jewish world. One of the first attempts at making Judaism more universal occurred when the Jews of Alexandria first translated the Bible into Greek. The end-product of this venture was a literary masterpiece known as the “Septuagint,” deriving from the Greek word “seventy,” named after the seventy elders who helped articulate Moses’ message to the people after the revelation at Mt. Sinai.
From the view of its original team of translators, these Alexandrian Jewish scholars believed that the translation of the Bible would serve to not only make the Bible more understandable to predominantly Greek speaking Jewish audience, it would also serve to make Judaism more intelligible and respectable to the gentile community.
But there may have been a more subtle goal. More than anything else the Alexandrian Jewish leaders wanted to promote an image of Judaism that did not suffer from parochialism. These men possessed a global-minded vision of Judaism as an international faith that could attract the best minds of the Hellenistic and pagan worlds. They believed that as a universal faith, Judaism could unite all the families of humankind. In fact, many Greeks came to embrace Judaism as their new faith. If you examine many of the rabbinic names in the first century C.E., there are quite a number of Greek sounding names, e.g., Antigonous, Alexander, Dosa, and Onkelos–attesting to the fact that Judaism expanded its population growth in the days of Late Antiquity by welcoming proselytes.
Philo of Alexandria, Judaism’s greatest Jewish philosopher of the first century (an older contemporary of Jesus), used the Septuagint to expound the message of ethical monotheism that is the foundation of Jewish ethics and theology.
Just imagine what a curious non-Jew must have thought when he heard Philo expound these famous words in his short but poignant work, “Nobility.” In this pericope, Philo stresses the importance of equal treatment of the outsider who comes to embrace the Judaic faith; the mark of the pious man is not “good birth,” but rather the individual’s virtue. Anyone familiar with the biblical narratives knows that even some of the greatest men of antiquity often sired sons like Cain, Ham, Esau, and others. In short, if Abraham could become a convert to the monotheistic belief in an ethical God, then surely other people could also make that same decision. In his closing paragraph, Philo adds:
We should, therefore, blame those who spuriously appropriate as their own merit what they derive from others, good birth; and they should justly be regarded as enemies not only of the Jewish race, but of all mankind; of the Jewish race, because they engender indifference in their brethren, so that they despise the righteous life in their reliance upon their ancestors’ virtue; and of the Gentiles, because they would not allow them their need of reward even though they attain to the highest excellence of conduct, simply because they have not commendable ancestors. I know not if there could be a more pernicious doctrine than this: that there is no punishment for the wicked offspring of good parents, and no reward for the good offspring of evil parents. The law judges each man upon his own merit, and does not assign praise or blame according to the virtues of the forefathers.
There can be no doubt that Philo envisioned a day when Judaism would win the hearts of humankind, and would eventually prove to truly become a light unto the nations of the world, as Isaiah foretold (Isaiah 49:6).
The NT bears witness to the phenomena of Jewish proselytizing and one can easily see how early Christianity incorporated much of first century’s Jewish activity, making it a part of their own modus operandi. The Gospels attest that the Pharisees “compass sea and land to make one proselyte” (Matt. 23:15). Most Christian scholars see this passage as a rhetorical exaggeration, but one must seriously wonder whether this observation is indeed correct. Josephus himself observes that Judaism in his day appealed to Greek and barbarian cities alike.
Historians observe the even in the centuries that followed the great destruction of the Temple, 10% of the Roman population was Jewish—an astounding statistic! Based on the number of Jewish catacombs found in Rome, there were about 100,000 Jews who had either settled or converted to Judaism in the early centuries both before and after the Common Era. 
Judging from the literature of that era, one may surmise that the Roman population probably found the Jews to be an intriguing ethnic group in their encounters. The Romans, much like Americans today, probably found the Shabbat discussions on the Torah to be interesting and provocative. The Jewish community proved to be cordial and hospitable with their Latin and Greek speaking guests. The intellectual ambiance evidently attracted many new converts to the faith. The early Christian church once had some real competition from the Jewish community—of all people!
Roman philosophers, writers, and politicians often complained about how the conquered people of Judea behaved more like the conquerors! According to the Roman historian Tacitus, he was very disturbed at the proselytizing efforts made by Jews which he regarded as a threat to the Empire. One Roman Empress, Poppaea Augusta Sabina (the second wife of Emperor Nero) was a close friend of Josephus and she is credited with building a synagogue; in addition, contrary to Roman custom, she was buried instead of cremated—more in line with Jewish tradition.
The Roman satirist Juvenal (60-130 C.E.), likewise expresses outrage at the spread of Jewish families among the aristocracy of Rome. He regarded Judaism as a mystery religion, and believed the Jews worshiped the clouds on the Sabbath. The Roman Stoic philosopher Seneca and adviser to Emperor Nero was hardly any better and noted, “ The customs of this accursed race have gained such influence that they are now received throughout the world. The vanquished have given laws to their victors.” Some Roman thinkers considered Judaism on par with atheism since the God of Judaism is not visible.
As mentioned before in the “Groucho Marx Syndrome” posting, the time has come for modern rabbis to let go of the traumatized memories of Late Antiquity. In an open society, Judaism can greatly benefit from the energy, passion, and love of Judaism that so many of today’s Jews by Choice possess. In my Shul, over 40% are dedicated Jews by Choice. Anyone interested in learning about Judaism, feel free to contact me by sending me an email at this website.
For every Jew-by-Choice I welcome, I feel as a rabbi I am recovering lost souls taken away from us by Hitler and his eternal legion of Hitler-wannabees.
 Philo, “On Nobility,” Virtues 206-222.
 S. McKnight, “A Light among the Gentiles: Jewish Missionary Activity in the Second Temple Period” (Minneapolis: Fortress, 1991).
 Letizia Pitigliani, “A Rare Look at the Jewish Catacombs of Rome” Biblical Archaeology Review (May/June 1980), 43. Among the sarcophagi, she describes some of the ornate artwork that impressed her, “The most well-preserved fresco depicted a crudely painted Torah shrine (the Ark of the Law), its sacred scrolls flanked by the etrog, or citron; the shofar, or ram’s hoary; the lulav, a cluster of palm, myrtle, and willow branches; and a long-necked oil jar, a beaker and basin . . .”
 Menachem Sten, “Greek and Latin Authors on Jews and Judaism, Vol. 2″ (Jerusalem: Jerusalem Academic Press, 1980), 5.
 Cited from Louis H. Feldman, “Jew and Gentile in the Ancient World” (Princeton: Princeton, 1993), 491, n. 40.
This question is actually a response to history. You see, there was a time in Jewish history where we as Jews did seek converts. In the Bible, Abraham is said to have 'left with the souls he had acquired' which is interpreted by the rabbis as those whom he had brought under the then covenant between Abraham, his descendants, and God. Historically, we have good reason to believe that the Roman Empire was made up of a huge number (maybe even as high as 10% but I am dubious about this) of converts to Judaism. So what happened?
It became dangerous to seek converts for Jews. With the rise of Christianity and their ultimate acquisition of political power, Jews were seen as cursed and any rights afforded them came from 'Chrisitian charity.' In other words, Jews had fewer and fewer rights under the Church and, with the rise of Islam in the East, the Mosque converting out of Islam was literally a death sentence (which is exactly what happens in almost every Islamic-dominated country today). When these two competing religious systems which sought complete domination arose, it was clear that any converion to Judaism was a public slap int he face of denial to the 'new covenant' which could not be tolerated. And when someone did covert to Judaism or the Jews were seen as seeking coverts, it was always the Jewish communities which suffered. Simply put, it became dangerous for Jews to seek converts.
Since seeking converts to Judaism was repressed by the political authorities, conversion went underground to the extent that people converted secretly at times. But, with some exceptions, the general consensus was that non-Jews are not to be trusted even if they say they want to convert. (The Talmud calls those who seek to convert a 'sapachat' - a scab...ouch!). The Talmudic and Mediavel Jewish traditions are divided on how welcoming we should be to converts but that dispute comes from historical suspicion as to someone's motives. This suspicion came from history and from Jewish communities' own experience.
So, Jewish communities did what they always do when persecuted. They sought strength from within and excluded, as much as possible, converts from without. If someone wanted to become Jewish, that was all well and good, but they would have to show how commited they were to the covenant and how much they really wanted to belong to the people of Israel. That would take work, study, and commitment. If, after that time they were ready, they would go before the Beit Din and pass the test. Frankly, the rabbis made it as unattractive to convert as they could - that was the intent. No one would subject themselves to that unless they were really interested.
There is great wisdom in the what the rabbis did, mind you. Today, conversion to Judaism is much easier in almost every case but every rabbi can tell you stories of how they worked with someone who they thought was sincere only to find out that they dropped out of Judaism because they weren't satisfied. Our Sages did not see Judaism as a social club but rather as a covenant and they made it hard to belong. Rightly so.
We are living with that legacy today. Even though there is nothing wrong with advertising Judaism, we really need to ask the question: do we want people in the covenant who have not allegiance to the covenant? Ours is not a religion of belief - we have no belief dogma. Ours is a religion of family and peoplehood, of shared history and shared dreams and of Torah. One does not 'join' the Jewish people as one does another religion. There is no statement of catechism or declaration of faith that 'makes' someone Jewish. It is the very nature of Judaism that has given rise to the reality of how we seek converts. The covenant takes work and, to be a part of the covenant takes study and comprehension. There are no promises of an afterlife. There are no promises of riches. What there is is an eternal family of covenant. If someone seeks to take up that burden, the Jewish people is ready to teach. But since Judaism does not stress heaven and hell or, God forbid, make promises about them, then most people who are seeking religion will not look at Judaism for it offers challenge and reflection, not magical promises. The few who are so inclined to seek will find Judaism deep, broad and revelatory. Those who are looking for easy answers usually go somewhere else.
One final note: about 25 years ago, the head of the Reform movement, Rabbi Alexander Schindler spoke about the need to do active Jewish outreach. Because of his statement, the Reform movement has offered wonderful Introduction to Judaism class, Taste of Judaism classes, and has brought many many thousands under the covenant. But, at the same time, though we are free to come and go as we please from whatever religion we want, the Reform movement has seen the same things the rabbis saw so many years ago from time to time: those looking for easy answers were ultimately dissapointed that they did not find the magic they sought in Judaism and so left. The covenant meant nothing to them. That is precisely what our Sages were trying to prevent.
So the answer to your question is quite simple: we don't actively seek converts because we can't promise anything magical and our covenant is one that must be embraced with proven commitment, not imposed. Anything less treats Torah and the Jewish people, Jewish tradition and ritual as any other magical formula and that is unacceptable. That is why we don't actively seek converts.
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