It's quite likely Paul saw Jesus as ushering in the eschatological time foretold by the prophets in which the 'Gentile' nations would turn from their idols and embrace the one true God of Israel (cf Zechariah 8:20-23), and Paul saw himself called to this ministry. His objection was based on the belief that salvation was through faith in Christ. He opposed circumcison for Gentiles on the grounds that "... many peoples, and strong nations shall come to seek the Lord of hosts in Jerusalem" (Zechariah 8:22) and worship there
as Gentiles, not as Jewish converts.
Peter's vision in Acts 10 seems clear enough on that point.
It's worth noting that around this time, the Jews, too, were debating
the issue of Gentile inclusion:
"It was deemed unwise to reveal their laws to the Gentiles, for such knowledge might have operated against the Jews in their opponents' courts. Hence the Talmud prohibited the teaching to a Gentile of the Torah, "the inheritance of the congregation of Jacob" (Deut. xxxiii. 4).
...
Rabbi Emden, in a remarkable apology for Christianity contained in his appendix to "Seder 'Olam" (pp. 32b-34b, Hamburg, 1752), gives it as his opinion that the original intention of Jesus, and especially of Paul, was to convert only the Gentiles to the seven moral laws of Noah and to let the Jews follow the Mosaic law – which explains the apparent contradictions in the New Testament regarding the laws of Moses and the Sabbath."
The Seven Laws of Noah:
Not to worship idols.
Not to curse God.
Not to commit murder.
Not to commit adultery or sexual immorality.
Not to steal.
Not to eat flesh torn from a living animal.
To establish courts of justice.