Indeed, as a highly corrupt church with whom we can have no fellowship, and headed by "that antichrist" himself, but a church nonetheless. Thus I find myself disagreeing with the baptist idea of "it is no church at all."
It would seem that an entity that
1) is highly corrupt
2) with whom we can have no fellowship
3) headed by "that antichrist"
is not a church. How could we possibly have no fellowship at all with other branches of Christianity? In this, I assume you agree that someone in a Roman fellowship should not partake of the Lord's Supper in for example, an OPC church. Is that correct?
Couldn't we say points 1 to 3 apply to another religion entirely (e.g. Buddhism)?
We Reformed understand the distinction between the "visible" and "invisible" Church. There are individual Christians in the Roman communion. There are almost certainly some in non-christian religions (e.g. Someone gets saved today in a Buddhist Temple, and for a short time remains there).
But that is not the same thing as saying the ecclesiastical authority of the Church has the authority to perform or represent sacraments. That would seem, at least, to require a minister of the Gospel, the object of baptism. I don't see how any church can be a church without the Gospel. The Gospel is the spiritual basis of the invisible, universal church.
Finally, in a very practical way, what do you think of this: I, personally, was baptized in a United Methodist Church as a child. Now, I don't know what you know about the UMC, but
Actually, we have something in common. I too was so baptized and was an active UMC member.
I am aware of the falling away from the authority of Scripture within that denomination and the liberalism that now dominates it denominational polity. We both would no longer agree with the Arminian influence in the theology. However, we both know there is still a big block of Christians, God fearing people who believe the Gospel there. The Church still officially holds to the ultimate authority of Scripture and the Gospel (the four legs of the table of Mr Wesley). The UMC does not officially pronounce anathema on the Gospel, but nominally, at least still holds it.
So, like you, I understand a UMC infant baptism would be valid as a Christian baptism, to be administered but once.