That is both Biblical and doctrinally correct. Repentance is often seen in Israel's program, which Christ spoke to regarding the Kingdom of heaven (to be installed on the earth) and commented to the disciples that they sound repent and be water baptized in the name of the Father, the Son, and Spirit.
We, today, contrary to that, are saved by grace, and that by faith. Repentance is not a formula pattern by which we are saved today; like it was for Israel in the Gospel accounts (Matthew, Mark, Luke, John). When in Acts 26:20, where it mentions that the Gentiles, that whey should repent and turn to God, this account, although in Acts 26, stems from the time period of Acts 9, in which Paul is here giving another account of the voice and vision and appointment by Christ regarding his ministry for today to the Gentiles. Acts 26 is a further revelation by Paul to the reader - to King Agrippa - on the details of his ministry appointment to the Gentiles, etc. When we study the accounts of Paul in his early ministry, he first preaches the gospel of grace to the Jews, and then Gentiles, and at that early time, if a Gentile wished to believer, they would still be inclined to join the Jewish church of Messiah believers. That is what the repentance is attributed to for those early ministry years of Paul. But that was not the final pattern which later materialized, which we find in the later ministry journey of Paul, especially when the Jews stopped entertaining Paul's message of grace, then Paul began going directly to the Gentiles first, and making no difference between Jew and Gentile. By the time that occurred, then the pattern for salvation had been revealed to Paul by the Lord Christ Jesus (II Corinthians 12:1: It is not expedient for me doubtless to glory. I will come to visions and revelations of the Lord.)
It was those "visions and revelations of the Lord", in II Corinthians 12:1, which were further revelations to Paul for the pattern for grace salvation today which did not include repentance, per say, as an ingredient for salvation.
We first see repentance specially commanded to the gentiles in Acts 17, where Paul told the Athenians that God formerly "winked at" their ignorance, "but now commandeth all men to repent."
"Then Paul stood in the midst of Mars' hill, and said,
Ye men of Athens, I perceive that in all things ye are too superstitious. For as I passed by, and beheld your devotions, I found an altar with this inscription, TO THE UNKNOWN GOD. Whom therefore ye ignorantly worship, him declare I unto you. God that made the world and all things therein, seeing that he is Lord of heaven and earth, dwelleth not in temples made with hands; Neither is worshipped with men's hands, as though he needed any thing, seeing he giveth to all life, and breath, and all things; And hath made of one blood
all nations of men for to dwell on all the face of the earth, and hath determined the times before appointed, and the bounds of their habitation; That they
should seek the Lord, if haply they might feel after him, and find him, though he be not far from every one of us: For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring. Forasmuch then as we are the offspring of God, we ought not to think that the Godhead is like unto gold, or silver, or stone, graven by art and man's device. And the times of this ignorance
God winked at; but
now commandeth all men every where to repent:" (Acts 17:22-30)
Again, you wholly misrepresent Acts 26. Paul was indeed speaking of the time the Lord originally sent him to the gentiles. But what the Lord told him at that time was to tell them to "repent, and turn to God, and do works meet for repentance."
This is not a statement that salvation has any bearing on salvation, but that works are necessary in one who is saved.
"At midday,
O king, I saw in the way a light from heaven, above the brightness of the sun, shining round about me and them which journeyed with me. And when we were all fallen to the earth, I heard a voice speaking unto me, and saying in the Hebrew tongue, Saul, Saul, why persecutest thou me?
it is hard for thee to kick against the pricks. And I said, Who art thou, Lord? And he said, I am Jesus whom thou persecutest. But rise, and stand upon thy feet: for I have appeared unto thee for this purpose, to make thee a minister and a witness both of these things which thou hast seen, and of those things in the which I will appear unto thee; Delivering thee from the people, and
from the Gentiles, unto whom now I send thee, To open their eyes,
and to turn
them from darkness to light, and
from the power of Satan unto God, that they may receive forgiveness of sins, and inheritance among them which are sanctified by faith that is in me. Whereupon,
O king Agrippa, I was not disobedient unto the heavenly vision: But shewed first unto them of Damascus, and at Jerusalem, and throughout all the coasts of Judaea,
and then to the Gentiles, that they should repent and turn to God, and do works meet for repentance." (Acts 26:13-20)
