Yes, someone who hates God and is determined to renounce His authority over their lives is actually treating Him as their enemy. This is why the Bible says, "Anyone who chooses to be a friend of the (sinful) world becomes an enemy of God" (James 4:4).
And it's also true that "God hates the sin but loves the sinner." But have you ever asked yourself why God hates sin so much? There actually are several reasons—but one is because God hates what sin does to us. Let me illustrate it this way: Suppose someone you love very much was diagnosed with cancer. Would you love them any less? No, of course not. You would "hate" the cancer because of what it was doing to them—but you would still love them.
You and I have a disease that is far more devastating than cancer—a disease of our souls called sin. God hates what sin does to us, for it separates us from Him and it brings chaos and unhappiness to our lives. But God still loves us—and the proof is that He sent His only Son into the world to die for our sins.
Have you responded to God's love, by accepting the free gift of salvation He offers you in Christ? If not, make your personal commitment to Christ today. Then thank God with all your heart that while He truly hates sin, He still loves the sinner.