Pronouncing a definitive answer to the question of the audience of Paul's letters is difficult. At times, Paul seems to explicitly address Jewish Christians and, at other times, Gentile Christians. Many--if not all-- of Paul's churches were "mixed" congregations of both ethnic Jews and Gentiles (see especially Romans 16). This reality is the obvious by-product of Paul's "Jew-first" missionary principle in which the expansion of Christian followed the Jewish diaspora from urban center to urban center throughout the Roman empire.
Pauline Christians first met in diaspora "synagogues" - which were no more than houses where worshipers gathered. (There is no archaeological evidence for free-standing synagogue buildings or churches in Roman cities until long after Paul's time.) There is no reason to believe that the Christian "house" churches described in Paul's letters and the book of Acts patterned themselves around any other model than the Jewish synagogue.
Despite the fact that Paul's "churches" were populated by both ethnic Jews and Gentiles, his letters are always--first and foremost--informed by his mission as an "apostle to the Gentiles." Paul understood himself--and his prophetic call--as the harbinger of the great endtime ingathering of the Gentiles into the "people of God" that the Hebrew prophets had predicted.
Given this clear--and often stated--self-understanding, let me offer three simple rules for discerning Paul's audience in his letters:
(1) Unless otherwise noted, Paul writes to a Gentile audience.
(2) When Paul writes about "Jews," these references are most likely to Christ-believing Jews--including the Jerusalem church and other ethnic Jews--that were full participants in the various missions churches rather than to all Jews in general.
(3) Whenever Paul addresses his Jewish kinsmen (sometimes all ethnic Jews, more often Christ-believing Jews as determined by context), these statements are always the exception--and never the rule--to Paul's normal Gentile audience and these statements are always clearly delineated by direct statements or clear clues in the text itself.
Look at this example:
Mark my words! I, Paul, tell you that if you let yourselves be circumcised, Christ will be of no value to you at all. Again I declare to every man who lets himself be circumcised that he is obligated to obey the whole law. You who are trying to be justified by the law have been alienated from Christ; you have fallen away from grace. (Galatians 5:2-4)
These words make absolutely no sense if Paul's audience was a Jewish community in which the males had already submitted to circumcision. These words are only meaningful if directed to the Gentile males who were considering Jewish proselyte conversion.
In Galatians 5, Paul is not denying the Jewish obligation of circumcision. Rather he is arguing against the imposition of Jewish circumcision on Christ-believing Gentiles. He is making no statement about the covenant obligations of Jews, rather he is affirming his mission to include Gentiles "as Gentiles"--without Jewish proselyte conversion--in the ingathering of the nations to God. Audience is everything when interpreting this passage.
When visiting Jerusalem on two separate occasions, Paul did not compel the Gentile Titus to be circumcised, but he did compel (and seems to have performed the act himself) the Jewish Timothy to be circumcised. Is Paul inconsistent? In no way. Circumcision was a covenant obligation for Jews that Paul continue to recognize as valid and God-directed, but was never an obligation for Gentiles. Given this, it is clear that passages like Galatians 5 are addressed to Gentile Christ-believers and should be interpreted accordingly.
Whatever Paul says about the Jewish Torah and its obligations--especially the cultural identity markers of circumcision, Sabbath observance, and food regulations (kashrut)--it is significant to note that he (unless otherwise stated) is speaking to a Gentile audience upon whom falls no Torah obligations.
The question in Paul about Jews and Gentiles together in "one body" is the question of whether the endtime ingathering of the Gentiles requires Jewish proselyte conversion (washing, circumcision, Torah observance). Paul answers an emphatic "NO!" to this question. For Paul, "Gentiles as Gentiles" are included in God's "age to come" without Torah observance that never applied to Gentiles in the first place.
Paul's "apparent" repudiation of the Mosaic law--in Galatians 5 and similar passages--means one thing if directed toward Torah-observant Jews like himself, but it means an entirely different thing if addressed to Gentile converts who as part of God's final, endtime action in Christ are now included into the "people of God"--without taking on the specific obligations of Torah observance.