One of the things that needs to be emphasized when approaching the study of early Christianity is the fact that the early Christians, and the writings they produced, were part of a real world (for my course outline and discussion notes for Christian origins go here). Writings such as those found in the New Testament were not floating up in heaven somewhere. Instead, they were written by real people in real places. As a result, they both reflected and were products of broader social and cultural contexts, both Greco-Roman (or Hellenistic) and Judean.
On the one hand, it is important to consider the complicated conglomeration of things we scholars simplify with labels such as “Hellenistic (Greek) world” or “Greco-Roman world”. There is far too much to cover under such terms, but among the issues are the ways in which Hellenistic (Greek) culture came to prominent position in the ancient Mediterranean, something that I have discussed in a post on Alexander the Great (d. 323 BCE) and Christian origins (NT 1.2). You might also get a taste, but only a mere taste, of how complicated this world was by reading some of the posts in my category Greco-Roman Religions and Culture.
There is a sense in which dividing the Judean world from the Hellenistic world is itself a problem, since the two cultures were in interaction for more than three centuries before the emergence of the Jesus movement in Judea. A similar thing could be said of interaction with Roman (better: Greco-Roman) culture once the Romans were in charge of things (beginning in the second century BCE but climaxing with the imperial period, beginning about 31 BCE). The so-called Maccabean revolt of the 170s BCE, which I discuss in ‘Tis the season . . . : Jewish and Roman holidays, involved a sustained war arising from conflicts with certain actions by Hellenistic rulers and those Judeans who adopted certain aspects of Hellenistic culture. However, the relation between Judaism and Hellenism was by no means entirely hostile, and there were varying reactions by Judean individuals and groups to particular facets of Greek culture both within Israel and in the dispersion (cities across the Mediterranean). The fact that the Hebrew Bible was translated into Greek (a translation known as the Septuagint = LXX) beginning in the third century BCE is indicative of the less antagonistic interactions that were going on in various places.
This discussion of varying Judean responses to Hellenistic culture segues well into the second main cultural sphere: Judean culture. To understand a movement that began within Judaism, such as the Jesus movement, one needs to consider Judean culture in its many forms in the first and following centuries. This is a tall order, since Judaism itself was marked by a variety which I have discussed in posts including Let’s talk about sects: Diversity in Second-Temple Judaism (NT 2.3). The Jesus movement was just one among many groups within second temple Judaism and it is important to consider how to plot out these followers of Jesus in relation to others. As we shall soon see in the case of Paul and the situation at Galatia, even early followers of Jesus could have different answers regarding the relation between the Jesus movement and certain aspects of Judean culture (circumcision among them).
There is a sense in which a course on the New Testament or early Christian literature is, through and through, a study of these two worlds and the interplay between them. So we will continue to struggle with these issues for a while.