I got the following line from the movie Cowboys vs Alien.
God doesn't care who you were. He only cares who you are.
Taking it with a pinch of salt, I'd like to ask the community if this statement can be asserted with biblical sources.
Key Verses If any one is in Christ, he is a new Creation. Behold, the old things have passed away, the new is come.
As far as the east is from the west, so far has he removed our transgressions from us - Psalm 103:12
Interpretation So, the whole basis of the Gospel is grace - the unmerited favor of God towards sinners. Grace is the complete forgiveness of sin, and a core tenet of the Gospel is that God's grace is abundant. Put simply, there is no sin that God cannot forgive. (I know, somebody's going to link to the unforgivable sin of blaspheming the Holy Spirit, but that's not where I'm going.) In forgiving us, God's design is to make us a new creation.
Whether forgiveness means that the sin is forgotten or merely paid for is irrelevant to the original question - does God care about what we were? Not in the plainest sense, no. Its water under the bridge, so to speak.
If God's design then is that we are transformed into a new creation, it would seem silly to assume that God would spend much time caring about where we begin. Put another way, God is sufficiently focused on what he will make of us that it seems silly for him to focus on what we were when we came to him.
Now, here's where I'm going to shift from God's motivation to what I suspect is the real thrust of the quote - If God is more concerned about what he would make of us, then once we come to him, any time we spend focused on what we were is distraction. We feel guilt and shame, to be sure, but the awesome news that is the Good News is this - God has forgiven us.
I'm trying not to preach here, but the point is so basic I think it needs to be made: God has forgiven our sin. What we were is no longer relevant. (It may have consequences in the temporal - not arguing that, I'm just saying, God is making us new.) The theological import of the admonition is 100% right on - God doesn't care where we came from, because he wants to remake us into his new creation anyway.
One last avenue of argument - Temporal Omnipresence
Most Christians (Process Theologians excepted) would, I believe, argue that God is not constrained by time. Given temporal omnipresence, then, God would simultaneously see the sinner and the new creation. If God is outside of time, not part of the timestream if you will, then there is no past or present for God - all time happens at once. If that is the case, then it isn't possibly to for God to care where you came from or where you are going, because its all present tense to him. Being that God loves us, he must care for us as we are along.
Of course God cares who you were, just as much as He cares about who you are, and just as much as He cares about who you will become. Ultimately, God always cares, that is what Perfect Love does.
Psalm 136 says that His love endures forever as a refrain throughout. Dallas Willard says that "the first act of love is the giving of attention." God has been giving us His attention for a very long time, which is another way of saying that He has cared about us for a very long time. In fact, Love can do no other than to care, for love to be uncaring would be a contradiction.
Obviously God cared about who we were enough to want to remake us as new creations (2 Cor 5:17), and also cared about who we were enough to want to separate us from our sins "as far as the east is from the west."