I know the Pre-Chrisitan Romans have a less than sterling record when it came to tolerance of Judean people in their native province, but from what I understand Jewish Romans before and after the diaspora were not explicitly mistreated if they caused no unrest. Did the treatment of Jews worsen with the adoption of Christianity?
It is hard to define "worsen" but things were not good for Jews during the late Empire, when it Christianized. As an interesting side note first, Julian the Apostate, the last non-Christian emperor, attempted to promote the "traditional" religions of the Empire. This included supporting mystery religions like Mithraism, putting Roman paganism on a sounder footing (he promoted the adoption of Neoplatonism as an example), and allowing the Jews to rebuild the Temple in Jerusalem (even though Jews were less than enthusiastic to do so) which was destroyed by Titus in 70 CE. With Julian's death in 363, many of his religious programs were abandoned or suppressed by his successors who were all Christian.
On to the treatment of Jews in Christian Rome. To start, there was a number of Christian councils and synods that worked to separate Christianity from Judaism in a religious sense that went on to other Jews and restrict their rights. The Synod of Elvira in 305 disallowed intermarriage between Christians and Jews. In 341, the Council of Antioch forbade Christians from celebrating Passover with Jews. In 363, the Council of Laodicea forbade Christians from keeping the Jewish Sabbath. These are some examples. While they did not yet persecute Jews, they led to the clear differentiation between Jews and Christians that would help act as an othering mechanism.
There were also policies implemented by the Empire that were discriminatory. Constantine forbade Jews from owning Christian slaves or from circumcising their slaves. He also forbade the conversion of Christians to Judaism and sought to regulate and restrict Jewish congregations and religious services. Similar edicts and laws would be passed by succeeding emperors with more extreme ones occurring under the Theodosian Dynasty which made Christianity the official state religion of the Empire. For example, the Codex Theodosianus of 438 forbade Jews from joining the civil service, army, and law. Jewish religious institutions were suppressed or eliminated and Jewish courts had their scope of legal autonomy restricted. Synagogues were often seized by the state or allowed to fall into disrepair without the opportunity to repair them. Many more synagogues were converted to churches.
Finally, the accusation of deicide emerged in the later stages of the Empire, which would become one of the most inflammatory canards espoused against Jews in order to justify antisemitism during the Middle Ages but especially following the First Crusade.