I'm trying to understand paedobaptism, but once again, something like this comes up and confuses me.
If the point of baptism is to baptise into a particular church, then why is a person not re-baptised every time they become members of a new church?
If baptism does not baptise into a particular church, what is to keep this child from being baptised into the visible Church?
I was wondering the same thing, if we acknowledge that other churches are true churches how does this work? Would Jews not circumcise their child if they would not have been member of a local synagogue? What about Paul baptizing converts when he was traveling?
The question raised isn't answered with reference to infants, but to any baptism at all. You can't be baptized into "the visible church-universal" without being baptized into a particular visible congregation. And it makes no sense whatever to baptize someone into "the universal church (visible)," following which he's cast adrift into the sea. Baptism isn't about the individual Christian with no connection to anyone but Christ-mystical. (We cannot even effect such a thing, or even recognize it as a certainty.) Since we believe that particular churches are not disparate congregations, but belong to one another, one whole body, then the actions of one congregation are actions on behalf of the whole. So, we recognize that a person, once he is a member in a particular church, is admissible to another church of like faith and practice without having to begin anew, as if a neophyte.
Who is responsible for this child? I mean, what pastor and elders are responsible for him, if he is just baptized and passed off... to no one? Have they "done their job" with respect to him? That's possibly how the CalvaryChapel does things, for whom baptism is just another "personally meaningful moment" in someone's spiritual life. Those guys don't even record memberships. So what do they care for the average attendee, if he has been baptized or not? It makes no difference to how that church seeks to shepherd sheep. Who are their sheep? Do they even know?
Re. circumcision. There are both cultural and religious ties to circumcision, the disentangling of which is part of the transition to international-Christianity in the New Covenant. But in general, circumcision (in the Bible) was a religious function, performed under the supervision or approval of the religious order, not just a parental function or entrusted to a local handy with a knife. What did they do in extraordinary circumstances? I don't know. Under some circumstances or other, there would need to be some way to know if this man or that were circumcised. Prove it somehow: either by demonstration (probably least desirable to everyone), or according to religious records, synagogal or templar.
We know such family records were kept as vital statistics for many generations, which things were an important part of the Jewish return from the Exile. And the destruction of the 2nd Temple in AD70 wiped out a tremendous amount of the centralized record-keeping. But the bottom line was surely: to be a part of synagogue, you had to be circumcised. Besides, to not belong to synagogue was tantamount to rejecting Jewish identity. If they were rejecting that, why have the son circumcised?
Re. Paul's baptizing converts. Where does this happen, without the founding of a church? Perhaps the best known example of something close to the suggestion is the case of the Ethiopian eunuch. Philip is equipped for his service, as one under the direct authorization from Christ (who is moving his agent around as if by a teleporter). There is some anecdotal (extrabiblical) evidence that the Ethiopian went home thus empowered to organize the church in his country.
The bottom line is: there is no evidence that Paul or anyone else just evangelized and baptized people, and then went trotting off to fire up the next big thing, meanwhile expecting the lately-baptized to spontaneously organize or do anything else. If this had been the apostle's habit, there would be no churches, because that's not how humans operate, and that's not how the Bible teaches us the church came into being. Baptism is part of church-organization. It's the beginning of church-discipline.