The following chart is adapted from a chart in the ESV Study Bible, which was itself adapted from a section by D. A. Carson in the book Love in Hard Places. I found it to be very helpful to see the spectrum of beliefs represented during the first century that are mentioned or presupposed in the book of Acts and in the writings of Paul.

Identity Beliefs Examples
Gentile (professing) Christians The law has absolutely no claim on their lives. Presupposed in Rom. 6:1, 16.
Jewish and Gentile Christians Christians are not under the law covenant even though they are certainly not free from God’s demands. Kosher food laws could be observed and circumcision practiced as pastoral wisdom dictated. Paul (see 1 Cor. 9:19–23.)
Jewish Christians They understood and accepted Paul’s position, but their personal “comfort zone” was to be observant Jews, at least most of the time. Circumcision and kosher food laws are not necessary for salvation or maturity, and they shouldn’t be imposed on Gentile believers.
Jewish Christians Jewish Christians should observe the traditions of the Mosaic code, even if it was acceptable for Gentile believers not to see themselves as under its stipulations. Certain men from James? (Gal. 2:12a)
Jewish Christians Jewish Christians should observe the Mosaic code, and Gentile believers can come to Christ through faith alone. However, the really spiritual should want to obey the Mosaic law code (even if it wasn’t strictly necessary for salvation).
Jewish (professing) Christians The new covenant was a renewal of the old covenant. Jesus is the Messiah, but his life, death, and resurrection restored God’s people to faithfulness to the Mosaic covenant. Therefore, if Gentiles want to come to the Messiah, they must first become Jews (and be circumcised, observe kosher and Sabbath laws, etc.). ) “Judaizers” (see Acts 15:1–35Titus 1:10.)
Devout, non-Christian Jews Christians are mistaken about the identity of Jesus, and the Jewish boundaries should not be opened to the Gentiles. The circumcised (Rom. 4:12a ; see Acts 21:27–23:11)