I suspect that many of us find Mark’s comment (below) relevant and powerful because we’ve found that, most of the time, “hate the sin” has been more prevalent and obvious than “love the sinner.” We bear the pain that proves it.
But if we see sin as something that injures and effects us deeply, and which bothers God’s determination that we should become familiar with His love, then we can hate it in a way that exalts and prefers love and the experience of it, while blaming sin as the enemy of love. I think that’s what Jude had in mind when, by the Holy Spirit, he wrote:
Jude 1:21 Keep yourselves in God’s love as you wait for the mercy of our Lord Jesus Christ to bring you to eternal life. 22 Be merciful to those who doubt; 23 snatch others from the fire and save them; to others show mercy, mixed with fear—hating even the clothing stained by corrupted flesh. 24 To him who is able to keep you from falling and to present you before his glorious presence without fault and with great joy— 25 to the only God our Savior be glory, majesty, power and authority, through Jesus Christ our Lord, before all ages, now and forevermore! Amen.