The way I understand.It did not make one a physical member of Israel as a born again name.
It was a shadow that pointed ahead to the sufferings of Christ beforehand and the glory that did follow. The opening of the graves and the resurrection gate. Suffering as our bloody husband as shown in the parable of Exodus 4. The revealing of the first born like that parable of Isaiah 53:6. two working as one. Or like the parable of Abraham and Issac on the mountain. The gospel hid
Because Moses, the law giver used to represent the letter . .death . He did not honor God. God was to kill Moses's first born . The Holy Spirit used a gentile like with Ruth to reconcile the curse and repent.
And thou shalt say unto Pharaoh, Thus saith the Lord, Israel is my son, even my firstborn: And I say unto thee, Let my son go, that he may serve me: and if thou refuse to let him go, behold, I will slay thy son, even thy firstborn. And it came to pass by the way in the inn, that the Lord met him, and sought to kill him. Then Zipporah took a sharp stone, and cut off the foreskin of her son, and cast it at his feet, and said, Surely a bloody husband art thou to me. So he let him go: then she said, A bloody husband thou art, because of the circumcision. Exodus 4: 22-26
Twice to emphasize as a double portion he uses "bloody husband" to represent the suffering of Christ before hand and the glory of faith the salvation of our new souls.
Receiving the end of your faith, even the salvation of your souls. Of which salvation the prophets have enquired and searched diligently, who prophesied of the grace that should come unto you: Searching what, or what manner of time the Spirit of Christ which was in them did signify, when it testified beforehand the sufferings of Christ, and the glory that should follow.1 Peter 1:11
I would offer it was the Spirit of Christ working in Zipporah (leaping bird) that moved her to perform the good pleasure of God. A picture of us casting our anxiety at his feet the gospel