[quote="Phemie, post:17, topic:335720"]
I'm not sure the OP's question has been answered.
If I'm a nurse in the hospital and the child of an Anglican couple is ill and the parents ask me to baptize him, will the child be baptized Catholic because I'm Catholic or will he be Anglican because that is the parents' religion? I was told that by virtue of the fact that I'm Catholic the child will be Catholic. What if my intent is that the child will be Anglican as I baptize him validly with the Trinitarian formula?
True story, told to me by the priest himself:
He was doing his bi-monthly visit to a mission and there was a snowstorm. An Anglican family had gathered for the baptism of a child but, because of the storm, the Anglican priest was unable to get there for the service that Sunday. He called our priest to see if he would be willing to accommodate the family, many of whom had flown in for the occasion, and baptize the child. Father did so with the ceremony found in the Anglican Book of Common Prayer. Is the child Catholic or Anglican?
There isn't Catholic baptism and non-Catholic baptism. There is valid and invalid baptism...well, and also licit and illicit within the category of valid, but that isn't what I mean. It is kind of like the Mass: even if there are illicit elements to a Mass, if it is valid then the True Presence is the True Presence. The reverence due to the Blessed Sacrament is not less when the Mass where it was consecrated had elements that were less than optimal. No, the reverence due to the Blessed Sacrament is always exactly the same. Likewise, the dignity of the baptized is always exactly the same.
If the child's parents have him or her baptized, the child is baptized. If their intention is to bring the child up in communion with the Anglican Church and they do that, the child is Anglican. If the parents bring the child up in the Catholic Church, the child is a Catholic. The baptism of a Catholic needs to be duly entered into the registry of the Church, but it isn't that act that completes the baptism. Registration is administrative; it is the verification and proof of what has truly already taken place.
Now, if a baptized person has not been in communion with the Church, there are ways of establishing that communion in a formal way. That doesn't change their baptism, though, nor does it make them a "better class of citizen" within the Body of Christ. It makes their communion within the Body of Christ more in keeping with their baptism (which in an ideal world would be in communion with the Bishop of Rome for every Christian) that is all.
We want our separated brothers and sisters to become Catholic so that we can all truly be one, as we are meant to be. When they establish full communion with the Church, however, they don't become more brothers and sisters. They were always full brothers and sisters. When the baptized of other denominations join the Catholic Church, then so to speak they start living at home, and gain the full life of faith that the fact of their baptism always implied was theirs all along.