The answer is yes. I have heard it said that it is impossible to love and hate at the same time.1 It may be difficult to feel opposite emotions simultaneously, because we are finite in our emotional capacity. However, it is perfectly possible to intellectually affirm—and act based upon—love for an individual while simultaneously affirming hatred for his sin. Otherwise the godly prophet Amos would have been commanding something impossible when he said, “Hate evil, and love good” (Amos 5:15).
In reality, to love God and mankind is precisely to hate sin. Suppose you had a family member who was suffering from cancer (perhaps you do). Would you find it possible to love your family member and hate the cancer at the same time? To ask is to answer. Sin is a spiritual cancer that results in spiritual death (Romans 6:23), because it is opposed to God; we must hate everything that is opposed to God.
C.S. Lewis explained the situation in this way:
I remember Christian teachers telling me long ago that I must hate a bad man’s actions, but not hate the bad man: or, as they would say, hate the sin but not the sinner.
For a long time I used to think this a silly, straw-splitting distinction: how could you hate what a man did and not hate the man? But years later it occurred to me that there was one man to whom I had been doing this all my life—namely myself. However much I might dislike my own cowardice or conceit or greed, I went on loving myself. There had never been the slightest difficulty about it. In the very reason why I hated these things was that I loved the man. Just because I loved myself, I was sorry to find that I was the sort of man who did those things. Consequently, Christianity does not want us to reduce by one atom the hatred we feel for cruelty and treachery. We ought to hate them. . . . But it does want us to hate them in the same way in which we hate things in ourselves: being sorry that the man should have done such things, and hoping, if it is anyway possible, that somehow, sometime, somewhere, he may be cured. . . .2
Thankfully, God hated sin but loved sinners enough to send His Son to die for us (John 3:16; Romans 5:8-9).