I would argue politely that in Acts there's no evidence that infants are in the households. There are always qualifiers in Acts such that it's ones believing that are baptized. And if you believe maids should be baptized, then I wonder if all PB accept this. It's easier to consult Biblical criterion to know who's a believer than it is to figure out who's in the PB's view of the the new covenant.
Of course, any self-respecting PB would deny your contention that no infants were in any of the households mentioned. That it is empirically impossible to prove is conceded, but it is equally unprovable that no infants existed. Statistically, the weight falls on the side of there being children. Families with no children have always been the exception rather than the rule from the beginning of time. But some of us PBs don't base our position upon the debatable household baptisms.
And I'll repeat what I said earlier: "What I've also found that's fascinating to me is that all PB are CB, at least when it comes to deciding what adults should be baptized. Also, all of the Biblical examples used by PB as to why a non-believer might be part of the covenant is an example with an adult, not an infant. Yet, both of these approaches conflict with each other, and conflict with the PB position."
As you might expect, I beg to differ with this blanket statement as well.
The fact is, most all PB I know would point to 2000+ years of Israelic history to show that infants were included in the covenant; deemed members of the OT Church. The covenant sign was commanded to be administered to infants of covenant members upon penalty of expulsion for refusing to do so (Gen 17:11,14).
Now, referring back to my other response to you regarding this odious error of
presumptive regeneration, the circumcised children were NOT presumed to be 'saved' and neither were adults (cf. Gen 17:25; Jh 8:37; Rom 9:6,11-13). They ALL had to "circumcise the foreskin of their hearts" (Deut 10:16; Jer 4:4; Rom 2:28,29; Col 2:11). So, perhaps now you can understand my objection to
defining the NT covenant sign of baptism as "an outward sign of an inward reality". The covenant sign was never understood in that manner, i.e., as an irrefutable sign of any particular individual's salvation. It was a sign of God's covenant of grace/salvation with believers, although unbelievers, both adults who belonged to the nation of Israel, with whom God had established His covenant, and their children received the sign.
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