I finished Martin Goodman's Mission and Conversion. What I'll focus on in this post is the Noachide laws, the seven commandments that parts of rabbinic Judaism held were binding on Gentiles (whereas Jews had to keep the entire Torah).
In Babylonian Talmud Bava Kamma 38a, we see the assumption that most Gentiles did not obey the seven Noachide commandments, and Rabbi Joseph in Babylonian Talmud Avodah Zarah 2b goes so far as to say that the Gentiles "were so incapable of keeping the laws that they were released from them" (Goodman's words on page 115). While Rabbi Joshua b. Hananiah affirmed in Tosefta Sanhedrin 13.2 that "the righteous of all nations have a share in the world to come" (Rabbi Joshua's words), presumably by keeping the Noachide laws, Rabbi Judah in Tosefta Sotah 8:6 states that all of the Gentiles knew of the Torah in their own language and ignored it, and so they deserved to go to hell. Rabbi Judah's opinion implies that Gentiles were somehow obligated to the Torah. And, in Babylonian Talmud Hullin 13b, an opinion attributed to Rabbi Hiyya b. Abba in the name of Rabbi Yohanan says that Gentiles outside of the land of Israel are technically not idolaters but merely follow their own ancestral customs. According to Goodman, this "seems to imply that such gentiles should be allowed to practise paganism as long as they are outside the holy land" (page 119). And so there was some diversity within rabbinic Judaism on the Noachide laws.
On page 151, Goodman refers to the view that belief in the Noachide laws developed after Hadrian in the first century C.E. prohibited circumcision, as a way for the Jews to say that Gentiles could be saved apart from the ritual of circumcision. Goodman disagrees with this view because he thinks that state opposition should have stimulated missionary zeal among Jews rather than dampen it. But the view (which Goodman attributes to William Braude and J. Juster) does intrigue me because I wonder why Jews under Hadrian would want to show that Gentiles could be saved apart from converting to Judaism. Was it to convince others that Jews were not xenophobic, as they were often accused of being? Was it to garner support from Gentiles in a time when they (the Jews) were vulnerable?