I started Martin Goodman's Mission and Conversion: Proselytizing in the Religious History of the Roman Empire. Goodman's argument so far is that Jews before 100 C.E. did not have an agenda of seeking to convert Gentiles to Judaism. But does not Matthew 23:15 say that the Pharisees go about sea and land to make one proselyte? According to Goodman, that passage is referring to Pharisaic attempts to convert fellow Jews to Pharisaism, not their efforts to convert Gentiles. Goodman acknowledges that there were Gentiles who converted to Judaism, but there was ambiguity within Judaism about whether or not they were considered fellow Israelites as a result of their conversion.
Goodman surveys Jewish literature and concludes that Judaism before 100 C.E. largely believed that idolatry was stupid, but not prohibited to Gentiles. There were some strands (such as the Septuagint) which even encouraged the Jews to respect the names of Gentile gods. An exception would be the Wisdom of Solomon, which lambastes Egyptian idolatry. While there was a hope that Gentiles would convert to the worship of the God of Israel in the eschaton, they were not expected to do so in the present day and age. On pages 60-61, Goodman acknowledges that Jews may have even considered themselves "religious mentors" to Gentiles, as the Jews encouraged the Gentiles to admire the Jewish way of life, respect the Jewish God, and be ethical. But Goodman says that this is not "an impulse to draw non-Jews into Judaism in the present."
Goodman also does not think that the Jews' pagan contemporaries sought converts. While the Romans encouraged the imperial cult within the empire, they did not have a mission outside of its borders to win converts. And the Cynics were rather exclusivist.
There were a couple of interesting items in my reading. First, on page 24, Goodman mentions Plutarch's dismissal of the belief of Euhemerus that the gods were "ancient humans, deified by a grateful posterity for their great deeds". This reminded me of the Wisdom of Solomon's attempts to account for the origins of idolatry. Second, on page 54, Goodman states that Gentiles embracing monotheism would have had to leave Gentile society. I think this is because polytheism was an integral part of that society, even if there were Gentile thinkers who gravitated towards a monotheistic notion of the divine (without, of course, feeling that they must abstain from the public worship of the gods). Third, I appreciated Goodman's discussion about intimacy on page 25: "As in human friendships, not many people can strike up a close friendship with everyone they meet. Most people will remain neutral or mildly benevolent towards those with whom they have no time to forge a firmer bond."