This is a good question. If we define personality as the combination of characteristics or qualities that form an individual's distinctive character, then this idea is consistent with a biblical worldview.
According to the Bible, we are all unique, because of two reasons. First, God created people. Second, all people have different experiences and reactions to the world. The most famous passage on the first point comes from Psalm 139:
For you created my inmost being; you knit me together in my mother’s womb. I praise you because I am fearfully and wonderfully made; your works are wonderful, I know that full well. My frame was not hidden from you when I was made in the secret place, when I was woven together in the depths of the earth. Your eyes saw my unformed body; all the days ordained for me were written in your book before one of them came to be. How precious to me are your thoughts,[a] God! How vast is the sum of them! Were I to count them, they would outnumber the grains of sand— when I awake, I am still with you.
When it comes to the second point, the Bible is clear that people are also responsible for their actions. So, even though a person may have certain predispositions, he or she still have the responsibility and possibility to act in a way that is righteous, that is loving. This is why in the New Testament, there are many passages that command people to act in a certain way even in the most difficult situations. Here is what Ephesians 4 states:
Therefore each of you must put off falsehood and speak truthfully to your neighbor, for we are all members of one body. “In your anger do not sin”: Do not let the sun go down while you are still angry, and do not give the devil a foothold. Anyone who has been stealing must steal no longer, but must work, doing something useful with their own hands, that they may have something to share with those in need. Do not let any unwholesome talk come out of your mouths, but only what is helpful for building others up according to their needs, that it may benefit those who listen. And do not grieve the Holy Spirit of God, with whom you were sealed for the day of redemption. Get rid of all bitterness, rage and anger, brawling and slander, along with every form of malice. Be kind and compassionate to one another, forgiving each other, just as in Christ God forgave you.
This point needs to be emphasized to be consistent with a biblical worldview.