This notion always gives me pause. I think it's worth asking what one really means when one says it. If what one means by God's "unconditional" love is a relationship in which love is freely given, regardless of how much the recipient deserves or does not deserve it, that is one thing. If, however, this means or at least includes in its definition the notion that God's love will automatically save me and get me to heaven, even against my reluctant will, we have a problem.
God's love is indeed freely given to all and it comes in infinite supply. But why is that? It's because love isn't something God has, love is what God is. Love, says Thomas Aquinas with the same voice as Christ, means "to will the good of the other as other." Love is pure infinite act, not motivated by selfish desire for gain or reciprocation. Love is not an emotion, a transient experience, or a political buzzword. Jesus reveals that God "makes his sun rise on the evil and on the good, and sends rain on the just and on the unjust" (Matthew 5:45). This is because he is the perfect infinite Giver, and he thus gives of himself perfectly and infinitely.
But the question is, how is that gift received? The unavoidable truth is that human beings are truly free creatures, and we can ignore or reject even the most perfect gift of God's love. We do this through sin. Sin is not a "no no" or a "mistake." Sin is also not make believe. Sin is, by its very definition, the rejection of God's love, the divine life in us. It is a refusal to be like God as we are meant to be, a refusal by which we transform ourselves into takers instead of givers.
But Jesus loves me just the way I am, right? Again, it depends on what you mean by that. Yes, he loves the prostitute, the tax collector, the reprobate sinner. In fact, he states that he came not for the righteous, but for sinners. But he loves all of us sinners far too much to just leave us wallowing in sin and death. People love to point out that Jesus doesn't condemn the woman caught in adultery. But they sometimes forget that in the same breath he commands her to "go and sin no more" (John 8:11).
In the words of Oscar Wilde in Lady Windermere's Fan, "We are all in the gutter, but some of us are looking at the stars." As Father Vincent Serpa, OP puts it:
God does love us unconditionally in that he loves us even in our sins. But he cannot love our sins. He cannot love evil. He will always forgive us if we repent. To love him back, we must be free to choose to love him or not. Love cannot be programmed or forced. To love him is the greatest thing we can do for ourselves. But we can choose to not love him. Our choice to not love him does not diminish his unconditional love. But it certainly diminishes ours!
Bingo! Father Serpa hits the nail on the head here. Think of it this way. God's love is like an infinite ocean, an infinite gift of his very self that he desires to give to each and every one of us. But imagine that some people show up on the shore with nothing but a thimble with which to receive him. He'll fill whatever you bring him, but some may not even come to receive him at all. Some may turn their backs altogether and refuse God's unconditional love. Every time I sin, I turn away from him. Please pray for me that I'll give him everything today, and rest assured I'll do the same for you.