Actually maybe this is a case for thinking the book is about "God?"
Many times in the New Testament, Jesus tells his disciples that only children can get into heaven and that to get to heaven, one must think like a child. Children often freely accept parents love and have faith in them. Likewise Jesus is asking the disciples to freely accept God's grace through him.
That child, in essence, gets to truly be herself, because she is free to accept the love of her her adopted parents. Celie, on the other hand, is raised from the get go that she hasn't "earned love" because she's either ugly or hasn't done enough. But yet, she is still a child in some ways, where she seems open to greater things than what she has now. I think the fact she sees Olivia the way she does (rather than as a child of rape) is a great indicator of that.
So I agree with you skylark that she can see humanity.
You've made a really great connection with the New Testament there, Mrs P. And your comparison also makes a case for the fact that a child who hasn't been given unconditional love, even if it's just a matter of parents' love being freely given only when the child performs well or lives up to the parents' expectations ... may have a harder time accepting unconditional love from God, as an adult or near-adult. Not that it's impossible, at all, but the journey may be longer and more difficult.