First it is not Paul's gospel, it is the gospel of salvation through our Lord Jesus Christ.
Once again Paul did not rebuke Peter for straying from the gospel. Paul rebuked Peter for trying to force the old traditions and customs on new converts, and if you continue reading that chapter it says they all came together and decide what from the old mosaic laws we should still observe. That chapter had nothing to do with the teaching of the gospel message.
and they were told to observe food laws (no blood) before they could even enter a place of worship and teaching...
19 Therefore, my judgment is that we should not make difficulties for those of the Gentiles who turn to Yahweh,
20 But rather, write to them that they abstain from defilements: such as idolatry, from all sexual impurity, from that which has been cooked with the blood still in it, and from bloodshed by violence--
21 For Mosheh, from the earliest times, has in every city those who preach him, being read in the synagogues every Sabbath Day.
If thye continue to go to service they will learn everything else because;"
Mosheh,...being read in the synagogues every Sabbath Day."
"And he came and dwelt in a city called Nazareth: that it might be fulfilled which was spoken by the prophets, He shall be called a Nazarene." Matthew 2:23
"For we have found this man (Paul) a pestilent fellow, and a mover of sedition among all the Jews throughout the world, and a ringleader of the sect of the Nazarenes" Acts 24:5
Isayah 11:1-2, "There will come forth a Rod out of the stem of Yishai, and a Branch will grow out of his roots. The Spirit of Yahweh will rest upon Him, the Spirit of wisdom and understanding, the Spirit of counsel and might, the Spirit of knowledge and of the reverence of Yahweh."
Branch is word H#5342 - netser: a sprout, shoot
Original Word: נֵ֫צֶר
Part of Speech: Noun Masculine
Transliteration: netser
Phonetic Spelling: (nay'-tser)
Short Definition: branch
A "Netzer" is a type of Branch - a shoot from an olive tree that grows out of its original root system but springs up at a later time from the stump, or somewhat distant from the trunk.
"For we have found this man (Paul) a pestilent fellow, and a mover of sedition among all the Jews throughout the world, and a ringleader of the sect of the Nazarenes" Acts 24:5
("Netzer or Nazarenes" = "Branch/shoot" )
John (Yahchanan 15:4-6, "Abide in Me, and I in you. Just as the branch cannot produce fruit by itself, unless it abides in the vine, neither can you, unless you abide in Me. I am the vine, you are the branches. He who abides in Me, and I in him, produces much fruit; but without Me, you can do nothing. If anyone does not abide in Me, he is thrown away like a branch, and is withered; and they gather them and throw them into the fire, and they are burned."
Epiphanius (Fourth century "church father") writes of the ancient Nazarenes: But these sectarians... did not call themselves Christians--but "Nazarenes,”
Jerome (4th Century "church father") described these Nazarenes as those "...who accept Messiah in such a way that they do not cease to observe the old Law." (Jerome; On. Is. 8:14).
"Minæans" apparently Latinized from Hebrew MINIM (singular is MIN) a word which in modern Hebrew means "apostates" but was originally an acronym for a Hebrew phrase meaning "Believers in Yeshua the Nazarene."
Jerome responds saying of the Nazarenes "though believing in Christ, [they] were anathematized by the [church] fathers for this one error, that they mixed up the ceremonies of the law with the gospel of Christ, and professed their faith in that which was new, without letting go what was old."