How did Moses spread Judaism?

Answer 1

As persecutions forced the Jews to move to various countries, they brought their religion with them. Converts weren't actively sought, but there were some non-Jews who converted, including large numbers in a couple of instances (Exodus 12:38; and the Idumeans in the Hasmonean era. See also Esther 8:17).

Answer 2

Moses did not spread the religion of Judaism per se; he was not an evangelist. He was a prophet who revealed the Word of God to the Israelite people, a portion of whom would later become the Jews.

Answer 3

Judaism itself:

As the Jewish communities spread and moved. This phenomenon was set in motion by the various expulsions and persecutions, which drove Jewish populations to settle in new places.

Jewish influence:
As non-Jews came in contact with Jews, there was a degree of influence upon them. It was these Gentiles who were especially likely to adopt Christianity.

As the new religion of Christianity spread, it taught those beliefs which it had adopted directly from Jewish sources, such as the prohibition of infanticide and human sacrifice.

See also the Related Links.

Link: The diaspora

Link: The influence of Hebrew traditions on the Western world