There is one baptism. Of course someone who does not intend to baptize a person into full communion with the Catholic Church…but to say to baptize them as a Lutheran Christian…will not be baptizing them into full communion with the Catholic Church…
but it still the one baptism…thus a valid baptism is still baptism…even if done by an Buddhist who intends to make a person a Christian at his request…
Incorporated into the Church, the Body of Christ
1267 Baptism makes us members of the Body of Christ: "Therefore . . . we are members one of another."71 Baptism incorporates us into the Church. From the baptismal fonts is born the one People of God of the New Covenant, which transcends all the natural or human limits of nations, cultures, races, and sexes: "For by one Spirit we were all baptized into one body."72
1268 The baptized have become “living stones” to be "built into a spiritual house, to be a holy priesthood."73 By Baptism they share in the priesthood of Christ, in his prophetic and royal mission. They are "a chosen race, a royal priesthood, a holy nation, God’s own people, that [they] may declare the wonderful deeds of him who called [them] out of darkness into his marvelous light."74 Baptism gives a share in the common priesthood of all believers.
The sacramental bond of the unity of Christians
1271 Baptism constitutes the foundation of communion among all Christians, including those who are not yet in full communion with the Catholic Church: "For men who believe in Christ and have been properly baptized are put in some, though imperfect, communion with the Catholic Church. Justified by faith in Baptism, [they] are incorporated into Christ; they therefore have a right to be called Christians, and with good reason are accepted as brothers by the children of the Catholic Church."80 "Baptism therefore constitutes the sacramental bond of unity existing among all who through it are reborn."81