I have read all the proposed answers to this question and none of them are complete. Consider the answer I share deeply, because this information is not well known today.
God called Abraham when the whole world had turned against Him (Genesis 11:27-30). He promised that through his seed, all the families of the earth would be blessed. Abraham begat Isaac, "the son of promise," and Isaac begat Jacob whose name was changed to Israel, and from him the 12 tribes were generated. God called Israel to be His chosen people and that they would inherit the earth. The were placed above the nations (Gentiles) spiritually and politically. In the Millennial Kingdom of Christ, we see Israel ruling the nations, they are not equal.
Gentiles were "without hope and without God in this world" (Ephesians 2:12). Gentiles could approach God only by becoming proselytes by adopting Israel's customs and observing the Sabbath. Those Gentiles that got circumcised were considered "proselytes of the gate" and could enter the outside court area of the Tabernacle/Temple. Uncircumcised Gentiles could not enter the courtyard, and Jews would not even associate with them, let alone eat with them.
This is the situation when we come to the 4 accounts of our Lord.
Romans 15 8-11
8Now I say that Jesus Christ was a minister of the Circumcision for the truth of God, to confirm the promises made unto the fathers: 9And that the Gentiles might glorify God for his mercy; as it is written, For this cause I will confess to thee among the Gentiles, and sing unto thy name. 10And again he saith, Rejoice, ye Gentiles, with his people. 11And again, Praise the Lord, all ye Gentiles; and laud him, all ye people.
God had revealed He would call a people out of the nations for His own name. This was not new revelation,but was well known. Gentiles could become proselytes and share in Israel's blessings, and they would contribute physical goods in return. James recognized this in Acts chapter 15, at the Jerusalem Council, which was held over the debate of whether Gentiles were required to keep Israel's customs, including circumcision. I will come back to this point later.
Jesus was sent to Israel, the Circumcision, and not to Gentiles. When he sent the 12 and the 70 out to preach "the gospel of the Kingdom," he specifically told them not to go into the streets the Gentiles. Israel would be saved first, depending upon their repentance and acceptation of the Lord Jesus, then Israel would bless the nations with their spiritual riches.
Israel as a nation did not repent, but crucified her Messiah instead. On the cross, Jesus cried out "Father forgive them for they know not what they do." They did what they did out of ignorance, not knowledgeable defiance. So God answered His Son's last dying request. On Pentecost, Israel was reoffered the Kingdom, dependent upon their national repentance.
Pentecost was not "the birth of the Christian church" as is commonly taught. It is the reoffering of the Kingdom to Israel. Peter addresses Israel specifically 4 times in his Pentecostal prophecy in Act 2. Notice all through the first 12 chapters of Acts that nothing of the truths the apostle Paul taught are there! Nothing about justification, nothing about reconciliation, nothing about a heavenly inheritance, etc. All in Acts is related to Israel's calling.
The 12 apostles never left Palestine throughout the book of Acts, for Jesus explicitly commanded them to start on Jerusalem, then go to Sameria (still in Palestine), and then to "the limits of the land" (not to the ends of the earth, as it is wrongly translated.) The only Gentiles that were reached in the first 12 chapters of Acts were proselytes: the Ethiopian eunuch (Acts 8) and the Roman Cornelius (Acts 10,11). No non-proselytes (called idolaters by Israel) were reached.
Israel rejected the testimony of the Holy Spirit through the 12 apostles 10 times in the first 12 chapters of Acts. For this reason, God raised up Saul of Tarsus, to begin a new work among the Gentiles. In Acts 13:1,2 Paul was "severed" (not "separated")
from the Circumcision to go into the Gentiles. Notice Paul wrote that he was "severed for The Gospel of God" and that gospel was not new but was the fulfillment of previous prophecy, namely God calling out a people from the Gentiles.
The first non-proselyte to be reached was Sergius Paulus, and he was reached by the apostle Paul. The Jew Bar Jesus tried to interfere and dissuade the Roman procounselor, and Paul spoke judgement against him and blinded him "for a season." That was a sign that Israel would be blinded for a season while the Gentiles streamed into the widening Kingdom of God. In Romans 11:25 we read Israel has been held in abeyance until the fullness of the Gentiles comes in.
So let's put this together. God's promises to Israel cannot be abridged for it was an unconditional promise. They shall, eventually, inherit the earth and rule over the Gentiles. There is no equality between Jews and Gentiles in that scenario. But God is God of the Gentiles too (Romans 3:29). God had already provided for the Gentiles, and Paul was sent to make it happen.
By Acts 28, Israel had rejected the testimony of the Holy Spirit another 10 times outside the land of Palestine. Paul spoke the same judgement from Isaiah 6 that Jesus spoke during his earthly ministry, and from that time, Israel has been put on "pause."
The period of time we currently live in is not the subject of previous prophecy. According to the prophets, the Messiah would come, deliver Israel from her enemies, and immediately usher in his Kingdom which was the subject of previous prophecy. I Peter 1:9-13 speaks of this. During this time, God is building His church made up of only a small remnant of Jews and mainly Gentiles. Once the church is taken up to meet the Lord in the air, God will resume His dealings with Israel.
When did Jesus change his view of reaching Gentiles? Perhaps the answer is "never." Jesus ministered during the time when Israel was not held in abeyance. Because of God's promises to Israel, they had to reject the Christ so that the Gentiles could be reached. So the goal to reach Gentiles was always on the Lord's mind, but because of the promises, the Word had to go to Israel first. When Israel proved her apostasy throughout Palestine, God opened the door to the Gentiles (Acts 13:1,2). This is when the body of Christ began, but it was not yet a "joint-body." Israel still had preference over Gentiles at that time.
When Israel had fully proved her apostasy, in Acts 28:28ff, God revealed secrets He kept from before the creation. Those secrets are revealed by Paul in Ephesians chapters 1 and 3. The Secret of Christ in Ephesians 1:9,10 revealed that Christ would not only inherit the earthly jurisdiction, but he would reign over the heavens too. Absolutely nothing about the heavenly jurisdiction was made known in previous prophecy. The Secret of Christ was revealed because the Christian's heavenly inheritance was also revealed, and God wants us to know Christ will head up all in heaven as well as on earth.
The joint-body of Christ began in Acts 28:28ff with the revelation in Ephesians 3. Jews and Gentiles are fully equal in this joint-body and, since God gave Israel jurisdiction of the earth in Christ, He could not give Gentiles an earthly inheritance. The joint-body of Christ inherits the celestial realm, not the earthly Kingdom. We are not Israel, but are a separate body of believers.
Most of the verses I have mentioned should be well known to people on this forum, but if you need help or clarification, or you want to dispute lovingly, leave a comment I will answer.