At one time I was very turned off by that expression. What exactly is a baby Christian anyway? From what I have seen over the years it must refer to the people who walk out of the church before the service is over after feeling that the Pastor had referred to them as such.
Today I have discovered the magic associated with the phrase. Oh, I better be careful not to mention the word magic around mature Christians. They have the tendency to associate the word with the demonic. Makes you wonder who really are the babies?
Any how, today I received a epiphany! Jesus said that we must come to him as a child. Being a baby or child is exactly what we should be upon our acceptance of Christianity in our lives. We must be a blank canvas. As he said, we can’t put new wine into old wine skins or the old wine shins will burst. This means that as we, mature Christians (LOL) concentrate on holding on to our old ways we leave no room for the new.
You see, the Kingdom is constantly growing and advancing. Christianity is not finished yet. It is a work in progress!
The Intuitive Life Coach 
I see the point you’re making though it doesn’t make me any more fond of the term. More so, I’ve always hated “pre-Christian”. Both imply that there is a certain way we should look as we mature in our spirituality. How pretentious to think that we know what that should be for each individual.
1 Corinthians 12:28 (New International Version)
And in the church God has appointed first of all apostles, second prophets, third teachers, then workers of miracles, also those having gifts of healing, those able to help others, those with gifts of administration, and those speaking in different kinds of tongues.
Ephesians 4:11 (New International Version)
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It was he who gave some to be apostles, some to be prophets, some to be evangelists, and some to be pastors and teachers,
“I like your Christ, I do not like your Christians. Your Christians are so unlike your Christ”. ~ Mahatma Gandhi