What Is the Relationship Between Being Jewish and Believers in Jesus?

In the earliest Gospels, Matthew, Mark, and Luke, we don't see Jesus violating the Jewish law in an obvious way. Paul seems to be wrestling with this question throughout his ministry of this relationship between being Jewish and believing in Jesus. The issue is about Jewish holidays and and eating may also come up in some of Paul's letters. And especially the critical issue in Galatians seems to be whether or not males who are not of Jewish birth need to be circumcised.