Fr. Robert Skeris writes:
Membership in the Church, which is brought about by valid baptism, makes one a part of the Mystical Body of Christ, the Priest, to whose priesthood one is interiorly conformed1 through the baptismal character.This is a point made by Sacrosanctum Concilium and repeated by many who use that document as a reference for explaining participatio actuosa.
In comparison with the high priesthood of Christ Himself, this priesthood of the baptized is analogous, by an analogy of proper proportionality.2 And since confirmation is related to baptism as growth is related to birth, it is clear that the so-called universal priesthood of all believers is ontologically based upon baptism, and not upon the sacrament of confirmation.3 As St. Jerome aptly phrased it, "Sacerdotium laici, id est baptisma."4
Mother Church earnestly desires that all the faithful should be led to that fully conscious, and active participation in liturgical celebrations which is demanded by the very nature of the liturgy. Such participation by the Christian people as "a chosen race, a royal priesthood, a holy nation, a redeemed people (1 Pet. 2:9; cf. 2:4-5), is their right and duty by reason of their baptism.It should be baptism and the gift of the Holy Spirit, whether by imposition of the hands or by the anointing by oil, that together lead to the third sacrament of initiation, the Eucharist. But given the historic separation of the first two sacraments of initiation by the Latins, they are stuck claiming that it is baptism alone.
If they were to return to the usage of scripture, baptism by water AND the Holy Spirit, with individual sacraments being returned as parts of the same ceremony as the norm, there could be some wiggle room for reinterpreting baptism in Latin documents in this way. But it would be better to admit that a mistake was made in their sacramental theology.