In short, no. But let me explain!
To start, here is what it says in the book of Romans:
12 It was said unto her, the elder shall serve the younger. 13 As it is written, Jacob have I loved, but Esau have I hated. Romans 9:12-13 (The “her” here is Rebekah, Isaac’s wife.)
To understand what this means we must do what Paul intends to his audience do: read the bible! This is from the prophet Malachi 1:2-3. Malachi is talking about Genesis 24 and the beginning of the people called “Edomites”. Here is what is says:
2 I have loved you, saith the Lord. Yet ye say, wherein hast thou loved us? Was not Esau Jacob's brother? saith the Lord: yet I loved Jacob, 3 And I hated Esau, and laid his mountains and his heritage waste for the dragons of the wilderness. Malachi 1:2-3
So, who is God talking to? This is a good question to ask when reading the bible. In this passage it is essential. God is talking to the Jewish nation around 460 BC. This was after the return from the Babylonian exile and the temple being rebuilt. Jacob and Esau lived just before 1800 BC. Around 1,400 years earlier. God very clearly is not talking to Jacob and Esau!
Why is God talking to the Jewish nation about these two? He is addressing what they did and how they lived, and instructing the Jews to live according to the law He gave them. In the lives of Jacob and Esau we see that it did not matter how they were born. Malachi says they are brother; twins in fact. The real difference between them was in how they lived and the legacy, or heritage, they left behind.
Esau’s heritage was the Edomites, from his nickname, Edom (Genesis 25:30). They were enemies of the Jewish nation. They were at war during all of Edom’s existence. King David fought them (see 2 Samuel 8:14), King Saul fought them as well (see 1 Samuel 14:47), and they were subject to the judgment of God (see Ezekiel 25:12-14).
In short, they were a stubborn people who refused the law of God, just like Esau did. So, God addressed the results of Esau’s life. He hated the results of Esau’s life.
How do we know God did not hate these people? First, in the very famous verse, John 3:16, God tells us He loves all people, even those who are His enemies. In Romans 5:10, God tells us He reconciled us while we were His enemies. No, then, God does not hate Esau.
What does this all mean? God pays attention to what we do and how we choose to live. We must live according to God’s word so that we can influence the world around us for God. This is so that we leave a heritage that reflects God. To live that way, we must walk out our God given destiny according to God’s will. Not perfectly, but in a lifestyle of repentance to God.