These are my thoughts semi-spinning off a seminar held at Wycliffe with the (very intelligent and well-read) Dr Benno van den Torren. It's quite possible I've mangled the arguments beyond recognition – if I've done so it's my fault.
Who makes decisions?
It's very interesting that the credobaptist movement only really got going during the Enlightenment, because it assumes some ideas which don't seem to have existed in the same way before then.
One of them is the notion of individual autonomy. In the modern world, we tend to think that the fundamental decision-making unit of society is the individual person, which incidentally is part of the reason for family breakdown and so on. Interestingly, the Bible teaches individual responsibility a lot, but doesn't teach individual autonomy, though we often read it back in from our culture.
Even in our culture, if we look at what actually happens with decision-making, not all individuals are autonomous. Some married couples or best friends always make decisions as a couple. Some types of disability mean that people depend on others for their decisions. The same could be said of some elderly people, who no longer make decisions for themselves, and some children, who do not yet make decisions for themselves.
In other cultures, it's even stronger. Some tribal cultures, the tribal chief will decide everything that matters. In some cultures, the corporation makes many important decisions. Where there is slavery, often the slaves do not get to make decisions for themselves, which is part of the reason we in the West hate the idea so much, because we value our own autonomy so highly. We even tend to describe relationships where one person does not have as much decision-making ability as we would like as “abusive”, but abusive relationships exist too.
Children are a particularly interesting example. The process of growing up, with all the stresses and strains of that, can usually be described in the (post-)modern West as going from the child having zero autonomy – they don't decide what to wear or where to go or anything to full autonomy.
So even in the West, the situation is a lot more complex than simply being individuals making their own decisions. There are still some corporate decision-making units, and there are lots of shades of grey.
The New Testament
The same was true in the Roman world in which the events in the New Testament take place. Slavery was very much legal, though with a large number of freedmen – ex-slaves. Wives and children were legally property of the husband / father, to the point where Paul could say that the difference between a slave and a son is that the son will one day inherit.
Some slaves do seem to have made their own decisions – Onesimus being a good example, even if he is most famous for running away, but there was wide variation in terms of both the educational level and the degree of autonomy that slaves had. Some were effectively estate managers, others were effectively treated as machines. Likewise with some wives – there are several places where Christian wives of non-Christian husbands are addressed.
What is interesting when we come to consider baptism in the New Testament world is that sometime individuals were baptised (for example the Ethiopian eunuch in Acts 8, who seems to have been a very powerful slave), and sometimes whole corporate units are baptised because the person in charge becomes a Christian.
One who heard us was a woman named Lydia, from the city of Thyatira, a seller of purple goods, who was a worshiper of God. The Lord opened her heart to pay attention to what was said by Paul. And after she was baptized, and her household as well, she urged us, saying, "If you have judged me to be faithful to the Lord, come to my house and stay." And she prevailed upon us.
Acts 16:14-15, ESV
There's no evidence of individual faith there from anyone in the household except Lydia. The household of a trader of purple goods would probably have included quite a few slaves and so on. Were there children? I don't think it matters. There's baptism without any record of individual profession of faith here.
And the jailer called for lights and rushed in, and trembling with fear he fell down before Paul and Silas. Then he brought them out and said, "Sirs, what must I do to be saved?" And they said, "Believe in the Lord Jesus, and you will be saved, you and your household." And they spoke the word of the Lord to him and to all who were in his house. And he took them the same hour of the night and washed their wounds; and he was baptized at once, he and all his family. Then he brought them up into his house and set food before them. And he rejoiced along with his entire household that he had believed in God.
Acts 16:29-34, ESV
Here, the whole household gets to hear, but only the jailer is recorded as believing, and the whole household gets baptised.
In that culture, it would have been very unusual for one of his slaves to refuse to go along with the master's beliefs. Which is why there's quite a bit in the New Testament about the difficult situation where a slave does become a Christian without the master doing so.
Other people who get baptised with their entire households: Crispus in Acts 18:8, Stephanas in 1 Corinthians 1:16. It's interesting that a decent fraction of all the baptisms we have recorded in the New Testament are baptising whole households. And whole households, not just everyone in the household except scullery maid number 3, who doesn't actually seem to have an individual faith.
The point is that baptism in the New Testament isn't just baptising people who believe; it also seems to be baptising anyone who is dependent on the believer for decision-making. They don't wait until the slaves profess individual faith or until they are free and so can believe without compulsion. If there were children in those households, would they have been baptised, or would they have waited? Waited for what? If slaves are being baptised, then children would be too.
The application to infant baptism today is obvious.