I don’t know a lot about this so I have to ask----
Regarding churches which do not use baptism and rely on the “sinner’s prayer” to convert people to Christ:
What do they do with the children who are raised in the church? Say a man meets some church people, says the sinner’s prayer and joins that church and he meets a woman who did the same—then they have children. If the church doesn’t do any baptisms, what do they do with the kids as they get older? I’ve never seen any sort of “Age of Reason Group Sinner’s Prayer Day” for children who reach a certain age. Do they just assume the kids are christian because they are raised in the church?
If so, what does this say about the sinner’s prayer?
Very few churches do not baptize. Most of the churches you have in mind baptize people after they have made a profession of faith. The “sinner’s prayer” is not given the formal status you seem to ascribe to it–what members of those churches (Baptists, etc.) would say is that people are saved by accepting Jesus as their Savior. You are right that in practice this is often ritualized as a “sinner’s prayer.”
Baptist and similar churches in the revivalist tradition expect the children of Christians to accept Jesus at some point, and this is usually followed by baptism. This may happen as young four (even three has been heard of), though six or seven is more common, and it often happens around 12 or 13. In my experience most children of devout evangelical parents have professed to “receive Jesus” by the time they reach high school age, but of course there are many exceptions.
Theoretically there is no difference between the experience of someone brought up as a Christian and someone coming to the faith as an adult. It is a central tenet of revivalistic evangelicalism (the kind of Christianity you’re talking about) that you can’t inherit the faith–being born in a garage doesn’t make you a car, etc. (Of course all Christians agree with this to some extent.) So in principle the child of devout Christian parents approaches Jesus in exactly the same way as those who have never heard of Jesus until they are adults.
My own experience is typical in some respects and highly odd in others. For one thing, my family actually didn’t put much stock in baptism–I was baptized at the age of 18, and my parents were baptized with me (my mother had never been baptized–my dad had been baptized as a child by a Methodist pastor and had also baptized himself after his evangelical conversion, but we weren’t sure these counted!). On the other hand, my folks didn’t like the “sinner’s prayer” because we thought it made conversion into a ritual (“easy believism” we called it) rather than a profound spiritual experience initiated by God’s grace. I claimed to have been “saved” at the age of four after a dream in which I saw my “black” heart turning white and awoke with the confidence that Jesus had forgiven my sins. As I got older I became increasingly aware that my experience really couldn’t be made to correspond with that of someone coming to Christ through a dramatic conversion, and my l attempts to “give my testimony” by telling the story of my dream as a four-year-old came to seem less and less convincing (at least to myself). This was one of the things that drove me toward a more traditional Christian soteriology.