So close. Soooooooooooooooooooo close.
Not even sure what this might indicate, or what I'm "close" to. You wrote of an "obligation" on the physical descendants of Abraham, and you appear to support the idea that this duty is without respect to faith. Well, I suppose if you tie circumcision to a covenant-of-works, this might make some sense.
Obviously, if God obligates something, it's sin to set it by. I am sure that the descendants of Ishmael were cut off from the covenant, because of their father. I'm sure the descendants of Esau were as well. The obligation to circumcise their children died with their fathers' being cut off or apostatizing.
Thankfully, there are descendants of both men who were reunited with the covenant of their father Abraham. How so? By faith, of course, and they took the sign when they rejoined the nation; but not because they were descended from Abraham, but because they were converts, adoptees.
Given my rejection that circumcision is in any way a covenant of works or tied to the original, but a sacrament of the covenant of grace, naturally I recast any idea of "obligation" in terms of faith. No obligation with respect to participation in the covenant of grace is bound upon parties who have abandoned even the external administration of it. First, attend the matter of reestablishing covenant relations with God; then go about fulfilling any obligations that entail.
But if the parents (whether believers or not) were part of the "visible nation of Israel", why shouldn't their children be circumcised?
Who says this couple or that aren't believers? Is this their public claim, or the determination of a court of the Law, or a hidden matter of the heart?
As you word the question, I interpret the proposal as the equivalent of "Shouldn't visible members of the NT church bring their children to be baptized?" Since any potential apostasy is hidden, if the members are not under any discipline or suspicion of false profession, I as a Presbyterian say those children you wrote of should be circumcised.
2Sam.15:17-22
And the king went out with all the people after him, and stopped at the outskirts. Then all his servants passed before him; and all the Cherethites, all the Pelethites, and all the Gittites, six hundred men who had followed him from Gath, passed before the king.
Then the king said to Ittai the Gittite, “Why are you also going with us? Return and remain with the king. For you are a foreigner and also an exile from your own place. In fact, you came only yesterday. Should I make you wander up and down with us today, since I go I know not where? Return, and take your brethren back. Mercy and truth be with you.”
But Ittai answered the king and said, “As the Lord lives, and as my lord the king lives, surely in whatever place my lord the king shall be, whether in death or life, even there also your servant will be.” So David said to Ittai, “Go, and cross over.” Then Ittai the Gittite and all his men and all the little ones who were with him crossed over [the Brook Kidron].
This Philistine of Gath threw in his lot with the people of God, particularly with their king the anointed one to whom he gave his allegiance. There is no reason to think this man, or his wife, or his
little ones had any lineal connection to Abraham. But these were now part of the visible nation of Israel, so surely he and all his house were circumcised.
It is not the case that some Israelites were circumcised out of a mindless ritual conformity to a covenant of works demand, and others were circumcised on account of faith. I find such a notion irreconcilable with biblical religion. It MUST be the case that some Israelites were circumcised for nothing but their heritage; but that is manifestly a corruption of a holy ordinance intended to mark out the household of faith.