Repschinski, Boris. "Chapter Seventeen: Purity in Matthew, James, and the Didache." in Van de Sandt, Huub & Zangenberg, Jürgen K. (editors). Matthew, James, and Didache: Three Related Documents in their Jewish and Christian Settings." Atlanta, GA: Society of Biblical Literature, 2008, 379-395.
Repschinski observes that purity codes have existed within Judaism and many other cultures, and that they tended to provide a good deal of social cohesion (Repschinski 2008, 379). Within Israel, purity codes related to Torah assist in defining a means by which we can be holy as God is holy (Repschinski 2008, 380).
Matthew's Gospel presents the idea of purity in terms of Jesus' work to bring forgiveness of sins (Repschinski 2008, 381). Jesus is presented as the one whose baptism and forgiveness actually takes away sins. He is the one who cleanses the unrighteous from the temple and who asserts the temple as the place of God's presence (Repschinski 2008, 383). For this reason, when Jesus leaves the temple, it signals the departure of God's presence. Jesus' presence, in Matthew's Gospel, remains in the Last Supper as the Passover is re-enacted (Repschinski 2008, 384). This, again, is a rite of purification. Jesus serves as the replacement of the temple. Repschinski notes that Matthew signals the extent of Jesus' replacement of a purity code by describing Jesus' interactions with Gentiles who would not be accepted in the temple culture (Repschinski 2008, 385). Matthew's orientation is that Jesus is held as the contrast to those who would violate the principles and spirit of Torah (Repschinski 2008, 386).
James, in contrast to Matthew, does not pursue issues of purity to a great extent (Repschinski 2008, 388). Ritual purity is absent from James' argument, though there are references to drawing near to God (Repschinski 2008, 389). There are multiple statements indicating a need to be in community with one another and with God. These are often made through descriptive metaphors (Repschinski 2008, 390).
The Didache teaches clearly that there is an expected code of purity. However, Repschinski observes a compromise. While all are expected to keep Torah, Gentiles are merely to do as well as they can (Repschinski 2008, 393). The purity in mind is not so much a ritual purity which guards worship, but a moral purity which breaks down barriers between people. Failure to pursue this moral purity can result in quarrels which, in turn, defile the ritual of the eucharist described in Didache 14 (Repschinski 2008, 394).