Finally, God commanded 4,000 years ago that the sign of the covenant be placed upon the males within the household of professing believers.
Weren't the adult males of pagan nations who wished to convert also candidates for baptism in order to "cut covenant" and enter the kingdom?
Although the sign of membership has changed from circumcision to baptism, God never rescinded the principle concerning the subjects who are to receive the sign and seal of the covenant promise. In the same way that all Israel was not Israel, all the church is not the church.
Because membership in the covenantal nation is conditional, therefore, one can be "of Israel" and yet, in the heart, be a son of the devil, or "not of Israel", covenantal sign notwithstanding.
Nonetheless, we are to place the sign of membership in the church upon those who qualify, per the instruction of God.
Some Baptists argue that baptism did not replace circumcision:
Though I think that baptism replaces circumcision, the Paedobaptist position does not require the premise. The reason being, Baptists and Paedobaptists agree that the visible people of God are to be baptized; so whether baptism replaces circumcision doesn't really matter.
Couldn't disagree more. Both circumcision and baptism have an outward significance. Have you ever wondered why in circumcision only males were circumcised while in baptism, both males and females are baptized. It is because both circumcision and baptism are testimonies to a greater truth regarding the economy of God.
Circumcision was not only the rite of cutting covenant, it prophesied the coming Messiah and the covenant He would make on behalf of the whole world. Thus, only males could be circumcized, pointing to the fact that the Messiah would be male, his blood was shed to point to the Blood of the New Covenant to be shed on the Cross, and His flesh was cut off to show that the Messiah would also be "cut off in the flesh".
In baptism, the rite points backward to the finished work of the Messiah. (Romans 6:3-5 and Gal. 3:27) We are made both participants on and witnesses of His Resurrection as we are placed under the water, showing His death, and raised to new life as He was.
This is why St. Paul so opposed the circumcision party -- not only would they be continuing the New Covenant which was to pass away, but every circumcision after the New Covenant would be saying to all watching that the Messiah was yet to come.
The only question is why are children no longer to be included among the visible people of God?
Why indeed! In the Old Covenant, the infant children were made full partakers of the benefits of the covenantal kingdom. How then do we exclude our children when the New Covenant is called "a better covenant which speaks of better things?" If it does less than the Old Covenant, then it certainly couldn't be called "better". This is the Baptist blind side, that they do not think in terms of covenant.
I would think that such a drastic change in covenant administration would be accompanied by some sort of explicit instruction.
Indeed. Yet there is a very clear absence of such changes in Hebrews.