In my reading today of The Cambridge History of Judaism, Volume 3: The Early Roman Period, I found information that related to Jewish attitudes towards Gentile observance of the Torah, which is an interest of mine.
First of all, on pages 899-900 of his essay "Philo of Alexandria", C. Mondesert states that the first century C.E. Jewish Hellenist Philo of Alexandria believed that the "Law of God, of nature and of Moses...should rightly govern the whole of humanity." Mondesert also states that Philo recognized that the religion of the Jews resulted in anti-Semitism because it separated the Jews from other people, and Philo's solution to this was a Messianism based, not on a conquering Messiah, but rather on "the adoption of the Law by the whole universe, the conversion of humanity to the God of the Jews and to that religion" (Mondesert's words).
Second, on page 944 of "The rabbi in second-century Jewish society", Shaye Cohen says that "The first century BCE and the first century CE were the heyday of Jewish proselyting", and that conversions to Judaism "abated in the second century", but did not cease. Elsewhere in this book (and I will not search for the place where, but it's in my notes), it has been argued that Jews became more hostile to Gentiles after the destruction of Jerusalem in 70 C.E., and I wonder if that could relate to the decrease in Jewish proselytizing (which may be a complex issue, period, since I have also seen references in this book to works that appear to challenge the notion that Judaism was ever a missionary religion). At the same time, for some reason, Cohen states on page 956: "The Fathers of Alexandria and the Rabbis of Palestine shared a common vision. Each wanted to win the world over to the true faith, but neither would have been comfortable with a real mass movement." This is after 70 C.E. The context of Cohen's statement here is his discussion of how Judaism and Christianity combined secrecy with openness. His argument is probably that they were keeping secrets to avoid becoming a mass movement, even though they also wanted to "win the world over to the true faith".
Third, on pages 908-909 of "Josephus (CE 37-c. 100)", L.H. Feldman notes that Josephus' descriptions of Jewish law differ from that of the Mishnah, and one reason Feldman offers for this is that Josephus wants to show that Jewish law is just as righteous as the Noachide commandments, which Gentiles have to observe. For example, Josephus says that a judge accepting a bribe must be put to death, which is not in the Mishnah, and Josephus also equates abortion with infanticide, whereas the Mishnah "does not regard the unborn foetus as a human being and justifies killing it to save the mother if the majority of it has not emerged" (Feldman's words). (The references on abortion are Josephus' Against Apion 11.102, and Mishnah Nid. 5.3.) But the Noachide laws for Gentiles prescribe the death penalty for judges who take bribes, as well as prohibit abortion on the basis of Genesis 9:6 (b. Sanh. 57b), and Plato also (according to Plutarch's De placitis philosophorum 5.15) regards the fetus as a living being. According to Feldman, Josephus is trying to show that God's law for Jews is just as righteous as God's law for Gentiles. This relates to Gentiles observing the Torah in that Josephus assumes that Jews observe one set of laws, and Gentiles observe another, and yet Josephus is seeking to present both as righteous.