Yes, it is biblical in the sense that we are sinners, that we have sinned, that we do sin, and that God loves us and hates our sin.
The way this question is framed is the way it has often been used both in evangelism tactics and in order to paint a picture of God, who God is, and God’s love that is ultimately not biblical. So, as many hear that phrase, “God loves the sinner but hates the sin,” the reason that’s not entirely appropriate is because it’s not just the sin that God sends to hell. God sends sinners to hell. God has enmity with those sinners, and they have enmity with Him.
While God has a sort of general, universal love of benevolence that is manifested in a love of beneficence upon all creatures, there is only a special, filial, saving love upon His own children. And not everyone is a child of God. Only those who trust Christ by faith are given the right to become children of God (John 1:12).
So, it is not appropriate to say that God loves the sinner but hates the sin when it comes to everyone everywhere, without exception. But it is appropriate to say, when it comes to Christians, that God does love us as sinners.
We also need to keep in mind that the New Testament designation is that we are not sinners in the technical sense of the New Testament. We are sinful and we sin, but sinners are the designated ones who have not repented, who have not trusted Christ.
So, I would say that God loves the sinful who are repentant and trusting Christ, and hates our sin.