One of the problems when dealing with defining who the proper recipients are in baptism is the very definition of baptism itself. The standard “on the street” definition in Baptist circles, which is the predominant view in evangelical churches, is “the outward sign of an inward reality.” And this makes great sense to people who aren’t familiar with the Reformed perspective on baptism (which is drastically different from the Roman Catholic Church in which the Reformed view denies baptismal regeneration).
From this article, here is how Calvin defines baptism, from the Institutes:
“the sign of the initiation by which we are received into the society of the church, in order that, engrafted in Christ, we may be reckoned among God’s children” (Inst.4, 15, 1).
As noted in the article, this stands in contract to the definition put forward by Stanley Grenz who defines it as the following:
“a public affirmation of a person’s conscious decision to place himself or herself under the lordship of Jesus” (Grenz 684 emphasis added).
“God-given means whereby we initially declare publicly our inward faith” (Grenz 689).
The writer of the article then concludes the following:
“He goes on to declare that ‘believer’s baptism is obviously superior” on the grounds that infant baptism ‘simply cannot fulfill this function’ (Grenz 689). He is in one sense quite correct. If baptism is all about a ‘conscious decision’ then Calvin has indeed ‘missed the boat’ with his advocacy of infant baptism. However, if baptism has more to do with signifying the cleansing of sin and being ‘reckoned among God’s children’ than it does with a ‘conscious decision’ then all should give careful attention to Calvin’s assertion that infants of believer’s must be baptized.”
Shifting from the Baptistic view to the Reformed or Presbyterian view can be a difficult shift for some though because of these assumptions and presuppositions about what the purpose, function and definition of baptism is. Before the Anabaptists came on the scene in the 16th century, this wasn’t questioned, although the RCC needed reformation on this point amongst many others, to be sure. Anyway, food for thought.