This is my first answer on /r/AskHistorians and I apologize if I do any of this incorrectly.

Unlike early Christians, in the 1st century C.E. the Jewish people were not a persecuted minority. Jews were an ethnic people who were still situated mostly in the Roman province of Palestine. The Jewish religion was still mainly focused on worship at the temple in Jerusalem, and discouraged converts. As a Roman province Palestine was forced to pay tribute to Rome which was a contentious issue for Jews and and especially Christian Jews who saw this as paying tribute to a foreign god.

Previously the governor of the province was a high ranking Jew, but after the first Jewish-Roman war in 73 C.E., a Roman was appointed. For the most part Jews were free to carry on their customs, and religious beliefs so long as they payed tribute to Rome. This is not to say Roman domination wasn't brutal, but it was no more brutal than any other Roman held province.

Source: Carr, David McLain, and Colleen M. Conway. An Introduction to the Bible: Sacred Texts and Imperial Contexts. Chichester, West Sussex, U.K.: Wiley-Blackwell, 2010.

*edited for clarity

"The Jews have long been in revolt not only against the Romans, but against humanity; and a race that has made its own a life apart and irreconcilable, that cannot share with the rest of mankind in the pleasures of the table nor join in their libations or prayers or sacrifices, are separated from ourselves by a greater gulf than divides us from Susa or Bactra or the more distant Indies."

This quotation from the second century rhetorician Philostratus more or less sums up the problem the Romans (and the Greeks) had with the Jews. Whereas other cults could be easily integrated into the polytheism of Greece and Rome, Judaism maintained a monotheism that allowed no place for other gods. As a result, Jews were unable to participate in the civic rituals of sacrifice and feasting that united the citizens of Mediterranean cities. They were therefore viewed with suspicion, and there was often an uneasy tension between Jews and Greeks when the two groups shared a city. This was particularly the case in Alexandria, which had probably the largest Jewish population outside of Judea. There the conflicts between the Jews and Greeks were so bad that a legion was maintained in the city to maintain order.

But while the neighbors of the Jews might have persecuted them, the official Roman government position was one of tolerance. For the one thing the Jews had going for them that the Christians did not was that they were practicing the faith of their fathers, and this went quite a long way with the Romans, who valued tradition very highly. And so a compromise was reached: prayers at the Temple in Jerusalem would be offered for the emperor and not to him. The Jews would have a degree of local autonomy, and significant portions of Judea would be managed by Jewish kings, or tetrarchs, or the like.

But after the great Jewish Revolt of 69-73, the Temple was destroyed. After the Bar-Kokhba Revolt of 132-136 (which seems to have been a more serious revolt involving Jewish uprisings in Cyrene and Alexandria as well as in Judea), Jews were officially banned from living in Judea.

Most other minority religious groups were tolerated without a problem. Only the Christians and the Druids (whose supposed penchant for human sacrifice the Romans found distasteful and who seemed to be the instigators of Celtic uprisings) were really actively persecuted.

As far as sources go, Josephus' Jewish War is the most detailed account of the condition of Judea in the 1st century, and has a great deal of background information on Romano-Jewish relations. M. Goodman's The Ruling Class of Judea is a classic modern source on the same topic. For Roman paganism more generally, and how it incorporated other non Greco-Roman religions, R. MacMullen's somewhat rambling Paganism in the Roman Empire is a good start.