P(S)aul

According to Epiphanius (church father/saint), the Ebionites (an ancient Jewish sect) believed that Paul was not Jewish. Infact Jews today will also tell you the same thing. Just ask the center for Jewish studies "Paul was born pagan and converted to Judaism; or he belonged to Hellenistic Judaism which was regarded as an inauthentic kind of Judaism; he believed that the messiah had come and that the Law could be transcended in the new messianic age, his background had been in Jewish mysticism. "

19 For though I am free from all, I have made myself a servant to all, that I might win more of them. 20 To the Jews I became as a Jew, in order to win Jews. To those under the law I became as one under the law (though not being myself under the law) that I might win those under the law. 21 To those outside the law I became as one outside the law (not being outside the law of God but under the law of Christ) that I might win those outside the law. 22 To the weak I became weak, that I might win the weak. I have become all things to all people, that by all means I might save some. 23 I do it all for the sake of the gospel, that I may share with them in its blessings. - 1 Corinthians 9:19-23

The religion of the Old Testament is not Judaism. Judaism is the traditions of the elders which Christ condemns in the strongest of terms. And it's worth noting that Christ never ascribes to Himself the title "King of the Jews". The early converts were Jews by their being of the kingdom of Judah (or Judea). But Paul was not a Jew in this sense, he was born in Tarsus and was of the tribe of Benjamin and in that verse you alluded to conspicuously does not refer to himself as a Jew.

So we should avoid any suggestion that Christianity "came out of" Judaism or that the only difference between the two religions is the position on Christ (as is maintained by some).