In a Reformed church, we can be fairly confident that a child who desires baptism is desiring it for the right reasons because of the Reformed tradition’s emphasis on a serious and explicit church membership. This is actually completely overlapping with the emphasis on the Lord’s Supper, but because there really is more to church membership than participating in Communion, it is worth pointing out.
Church membership is really the meaning of church discipline. The Reformers all saw the right preaching and the right administration of the Sacraments as the marks of a true church. They mostly all saw church discipline as the third mark.
Church membership is an area in which I would say Baptists in particular (and even more particularly, Reformed Baptists) have made the greatest contribution in the Reformed tradition. We believe God marks the Church off from the world. There is a “who is” and “who is not” when it comes to the church.
The Church is marked by a confession of faith in Jesus as Lord, marked by regeneration, marked by fruit of the Spirit, marked by forgiveness of sins, marked by holiness, marked by all kinds of evidences of grace. The church is the workmanship of Christ Jesus who walks in good works. The church is the household of God.
And the world is not marked by those things.
This is the main reason I have settled on the Baptist position versus the Presbyterian position (and I think I like more Presbyterian preachers than Baptist preachers)- but we believe every single person we baptize has all those things in the previous full paragraph. In that way, baptism is God’s way of marking off His people from the world through the hands of the Church.
So if every single week we are teaching that the church is a defined people (as defined above), and if you’re not a part of the church you are going to hell (which is what not having all those things means), and in light of all that a child says they want to obey Jesus as Lord in baptism, how strange to tell them “not yet.”*
*I hope at this point it is clear that if your church is not being clear about all these doctrines, then even I might tell the child “not yet”