Canon law does not stipulate the baptized as proper subjects, but the “Christian faithful”. The Christian faithful are defined by canon law as:
Can. 204 §1. The Christian faithful are those who, inasmuch as they have been incorporated in Christ through baptism, have been constituted as the people of God. For this reason, made sharers in their own way in Christ’s priestly, prophetic, and royal function, they are called to exercise the mission which God has entrusted to the Church to fulfill in the world, in accord with the condition proper to each.
§2. This Church, constituted and organized in this world as a society, subsists in the Catholic Church governed by the successor of Peter and the bishops in communion with him.
Can. 205 Those baptized are fully in the communion of the Catholic Church on this earth who are joined with Christ in its visible structure by the bonds of the profession of faith, the sacraments, and ecclesiastical governance.
Can. 206 §1. Catechumens, that is, those who ask by explicit choice under the influence of the Holy Spirit to be incorporated into the Church, are joined to it in a special way. By this same desire, just as by the life of faith, hope, and charity which they lead, they are united with the Church which already cherishes them as its own.
§2. The Church has a special care for catechumens; while it invites them to lead a life of the gospel and introduces them to the celebration of sacred rites, it already grants them various prerogatives which are proper to Christians.
Can. 207 §1. By divine institution, there are among the Christian faithful in the Church sacred ministers who in law are also called clerics; the other members of the Christian faithful are called lay persons.
§2. There are members of the Christian faithful from both these groups who, through the profession of the evangelical counsels by means of vows or other sacred bonds recognized and sanctioned by the Church, are consecrated to God in their own special way and contribute to the salvific mission of the Church; although their state does not belong to the hierarchical structure of the Church, it nevertheless belongs to its life and holiness…
Can. 209 §1. The Christian faithful, even in their own manner of acting, are always obliged to maintain communion with the Church.
It’s clear that not all baptized people are the Christian faithful.
However, a person who is seeking full communion in the Catholic Church should receive the sacrament prior to making a public profession of faith when that profession takes place in the context of the Mass:
If the profession of faith and reception take place within Mass, the candidate, according to his or her own conscience, should make a confession of sins beforehand, first informing the confessor that he or she is about to be received into full communion. Any confressor wo is lawfully approved may hear the candidate’s confession.