Membership is unnecessarily muddy. I propose restoring a primitive, biblical view that accounts for regenerate church membership and guarding the table of the Lord.
The Church began at Pentecost with the command to "repent and be baptized" (Acts 2:38). There is a "sacramental union" between the "sign and thing signified" (WCF 27.2) such that baptism is itself called the "water of rebirth" (Titus 3:5) and the "washing away of sins" (Acts 22:16, see HC 73). It should not be delayed, the Ethiopian eunuch was baptized immediately after hearing the gospel and asking for it (Acts 8:36). The classical statement of the faith to be understood and recited by the recipient of baptism is the Apostles' Creed.
Infant children of believing parents are also proper subjects for baptism based on the promise of God to them (Acts 2:39). They are "included in the covenant and belong to the people of God" (HC 74) just like the circumcised boys of Old Testament Israel. Regeneration is ordinarily, but not necessarily, tied to the moment of baptism (WCF 28.5, 6).
Confirmation is "the renewal of the baptismal covenant" (EC 122). It is meant for those who have reached "years of discretion" (BCP) but not exclusively for young men and women. It is the visible step where a Christian's faith is deemed sufficient for the Lord's Supper. Many call this a "profession of faith," especially for older recipients. This is the ordinary logic in the western church, both Catholic and Protestant.
By contrast, credobaptist churches require this discretion before both baptism and the Lord's Supper. Paedocommunion churches require this discretion before neither baptism nor the Lord's Supper.
Confirmation
Local church membership entails the rights of the Lord's Table and subjection to the Keys of the Kingdom. A communicant must "discern the body" (1 Cor. 11:29) and examine themselves (HC 81; WCF 29.7), requiring a capacity of discretion. This spiritual maturity is intrinsically linked to church discipline, which guards the Table from the unrepentant (HC 85; WCF 30.3).
While the Keys are committed to church elders who make the judicial decisions (WCF 30.2), the entire congregation is active in the execution of discipline. Paul commands the "assembled" church to purge the unrepentant by withdrawing fellowship (1 Cor. 5:5, 11). The elders pronounce the sentence, but the communicant members must follow through.
Therefore, baptized children are Christians and covenant members, but not active, communicant members in the local church. They are disciplined by their fathers (Eph. 6:4) and cannot take the Supper. They lack the maturity to either be subject to formal church discipline or to bear the burden of enforcing it upon others. Table access and church discipline are inseparable. The category of "junior member" or "non-communicant member" only adds confusion and ought to be avoided.
Put another way, Baptism brings a person into "the" church (universal). Confirmation brings a person into "this" church (congregation). The distinction in terms comes across in the E&R Book of Worship:
At Baptism: "Receive him, O Lord, into the fellowship of thy church, and grant unto him life everlasting through Jesus Christ our Lord. Amen."
At Confirmation: "I now receive and welcome you into the fellowship of this congregation, and invite you to partake of the Holy Communion, and to participate in all the privileges and obligations of the Church of Christ."
Following these principles, the order always remains: baptism, confirmation, membership.
Baptized immediately, instructed in the faith, confirmed at the age of discretion, and received into membership.
Baptized: Instructed, confirmed, and received into membership.
Unbaptized: Baptized immediately, instructed, and received into membership.
A child able to articulate the Creed should do so, even if too young for formal confirmation.
Unbaptized: Baptized (believers'), instructed, confirmed, and received into membership.
Baptized, Unconfirmed: Instructed, confirmed, and received into membership.
Baptized, Confirmed: Received into membership.
Evaluated on a case by case basis.
Those permanently lacking the capacity to profess the faith should be baptized at any age based on the belief of a parent, exactly like an infant. Communion, by contrast, requires the possibility of discipline. Parents and elders must weigh this carefully: offering the Table means declaring a willingness to hold that person formally accountable for sin. If the handicap precludes such accountability, it precludes communion. Withholding in these cases should never be considered disrespectful.