Romans 4 v.11 He [Abraham] received the sign of circumcision as a seal of the righteousness that he had by faith while he was still uncircumcised. The purpose was to make him the father of all who believe without being circumcised, so that righteousness would be counted to them as well, 12 and to make him the father of the circumcised who are not merely circumcised but who also walk in the footsteps of the faith that our father Abraham had before he was circumcised.
Clearly, Ishmael's circumcision did not carry the significance of Abraham's circumcision. What counted was the circumcision of the heart. Ishmael's heart was uncircumcised and he had no faith. All it showed was that he was physically (not spiritually) related to Abraham and a part of that community. Abraham's servants also were circumcised and we cannot assume they all had faith. The promise in the Abrahamic Covenant that God would be a God to them was true only for Abraham's children who had true faith. We cannot honestly say that God was a God to Ishmael as he was to Abraham. He is called the God of Abraham, Isaac and Jacob not the God of Abraham, Ishmael and Esau.
Joe said: Gen 17:10f This is my covenant, which ye shall keep, between me and you and thy seed after thee (Ishmael is Abraham’s seed)every male among you (Ishmael is a male) shall be circumcised (Ishmael was circumcised). And ye shall be circumcised in the flesh of your foreskin; and it shall be a token of a covenant betwixt me and you (Abrahamic Covenant). The fact that Ishmael was circumcised revealed that he was a member of the Abrahamic Covenant.
You have chosen to ignore those verses that clearly demonstrate that God had not established his covenant with Ishmael, even though Abraham was commanded to circumcise him.
Genesis 17:17 Then Abraham fell on his face and laughed, and said in his heart, "Shall a child be born to a man who is one hundred years old? And shall Sarah, who is ninety years old, bear a child?" 18 And Abraham said to God, "Oh, that Ishmael might live before You!" 19 Then God said: "No, Sarah your wife shall bear you a son, and you shall call his name Isaac; I will establish My covenant with him [not Ishmael] for an everlasting covenant, and with his descendants after him. 20 And as for Ishmael, I have heard you. Behold, I have blessed him, and will make him fruitful, and will multiply him exceedingly. He shall beget twelve princes, and I will make him a great nation. 21 But My covenant I will establish with Isaac, [not Ishmael] whom Sarah shall bear to you at this set time next year."
Abraham had begged God that Ishmael would live before Him and was told that God would NOT establish his covenant with him. He did however establish "an everlasting Covenant" with Isaac, or more accurately Christ who was to come from that line. These Galatian verses also show that Ishmael is in a different covenant than Isaac.
Galatians 4:22 For it is written that Abraham had two sons: the one by a bondwoman, the other by a freewoman. 23 But he who was of the bondwoman was born according to the flesh, and he of the freewoman through promise, 24 which things are symbolic. For these are the two covenants: the one from Mount Sinai which gives birth to bondage, which is Hagar--
Do you believe that Ishmael was in the Covenant of Grace? God shows grace only to His elect, so how could an unbeliever even be in that Covenant? And even more importantly, when you baptize an infant, do you say he or she is "in the New Covenant" or is "in Christ"?