If parallel worlds exist, I wonder what would the world be like if Judaism became one of the world’s largest religions? The question for some people may seem kind of funny. Can you imagine donating money to the government so that they could print the pictures of your parents or grandchild’s Bar Mitzvah on the national currency? But on a serious note, ask yourselves this question: Why didn’t Judaism attract the same following that Christianity and Islam later achieved?
Interesting question, no?
Historically, there was a time when Judaism during the days of Late Antiquity went out of its way to welcome non-Jews to Judaism. A sizable portion of the Roman Empire had Jewish citizenry. The Jews of Alexandria specifically translated the Tanakh into Greek to help attract new converts to the faith. Jewish thought made philosophers like Philo of Alexandria and Aristobulus popular scholars the Graeco-Roman world enjoyed reading.
Yes, the Alexandrian Jewish community envisioned Judaism as a universal faith–a view that most the rabbis did not share because of their hatred of Hellenistic culture. Jewish efforts to proselytize gentiles was so successful that the Roman Senate decided to expel the Jews in the year 139 B.C.E. and later in the year 19 C.E., according to Josephus (Josephus, Ant. 18.81–84). Incidentally, the NT indicates that the Pharisees of Jesus’ time engaged in outreach efforts to bring in new proselytes, thus we read, “Woe unto you, scribes and Pharisees, hypocrites! For you compass sea and land to make one proselyte” (Matthew 23:15).
With respect to our original question: Why didn’t Judaism evolve into a much larger faith? In a nutshell, it had much to do with war, attrition, and internecine politics between the Early Roman Church and the synagogue. Basically, once Christianity became the state religion, proselytization became a forbidden activity for Jews to engage in. By many estimates, the Romans killed over 1.1 million Jews as a result of the failed Jewish rebellions against Rome. Exponentially, one million people could over a millennium result in hundreds of millions of people given enough time. Add to this another 97,00o that were taken captive by the Romans.
Philo writes that in his day, Alexandria had over a million Jews living in his city!  The problem of Jewish proselytization was an area that the historian Josephus had to tread lightly in his history of the Jews. If he endorsed proselytizing, Josephus knew the Romans would execute him. On the other hand, Josephus does explain that the “Jews gladly welcome any who wish to share their custom. Josephus is careful to note that Jews do not take the initiative in seeking out proselytes and that, in fact, they take precautions to prevent foreigners from mixing with them at random. Josephus himself makes a point of stressing that while he was general in Galilee, when the Galilean Jews tried to compel some non-Jews to be circumcised as a condition for dwelling among them, he refused to allow any compulsion to be used, declaring that everyone should worship God in accordance with the dictates of his own conscience.”
Josephus, in his Antiquities 20:1, details how Queen Helena of Adiabene, and her son Izates, changed their course of life, and embraced the Jewish customs after meeting a Jewish merchant named Ananias, who influenced them to embrace Judaism. Louis Feldman writes in his classical study, “Jew and Gentile in the Ancient World” that the extent of proselytizing was not as extensive as the Roman satirists portrayed. Economics often played a major motivational role in these conversions. 
Historian D. Mendels writes, “The reason for such a law is quite clear. The Christian emperors wished to protect the state religion from fierce competition with Judaism; Sozomenus in book III.17 says this very plainly: ‘For, as the emperors were desirous of promoting by every means the spread of Christianity, they deemed it necessary to prevent the Jews from proselytizing those whose ancestors were of another religion […] for it was by conversion from the pagan multitudes […] that the Christian religion increased in numbers.’ Theodosius II in a law of 409 says emphatically: ‘It does not trouble us to admonish repeatedly, that those imbued in the Christian mysteries shall not be forced to adopt the Jewish perversity (Perversitatem Iudaicum), which is alien to the Roman Empire and adjure Christianity.” 
(More to come)
 Josephus, War of the Jews VI.9.3.
 Against Apion (2.261).
 Ibid., 2.257.
 Louis Feldman, Jew and Gentile in the Ancient World (Princeton, NJ: Princeton University, 1993), 333.
 Philo, Against Flaccus 6.43.
 D. Mendels, Memory in Jewish, pagan, and Christian societies of the Graeco-Roman world. Library of Second Temple Studies Vol. 45 (London: T & T Clark International, 2004), 119.