I'm glad you included this, because it answers the rest of your post.
The ancient Romans practiced both surgical and chemical abortions. They also did leave imperfect babies to the elements to die.
Yes, Christians rescued those babies and raised them as their own (which meant, remember, nursing Christian mothers sucking these unwanted babies on their own breasts).
When the pagan Romans discovered this practice, they accused Christians of cannibalism--that the Christians were using these babies in weekly orgies of drinking blood and eating flesh. In the mid-2nd century, a Christian named
Athenagoras stood before Caesar to defend Christians against this false accusation.
Athenagoras pointed out that Christians were even then preaching against abortion. His argument was, essentially, "You know we preach against abortion, so how could we also be killing babies ourselves?"
But this is the thing that the pagan Romans saw: Christians didn't just preach at pagans against abortion. They didn't even insist that Caesar change the laws to prevent abortion or save the children.
They went out and rescued the babies themselves.
When did you see Christians today do the same thing--standing at the abortion clinics saying, "Don't kill your babies--
we will take them!" It's not without evidence that pagans can quip, "Christians only care about babies until they're born."
Why did those Christians not implore Caesar to obey God? Because pagans are pagans, and Paul had already exhaustively explained that pagans
cannot obey God. Nowhere in the New Testament is the Church ever given the mission to fix the Roman empire, of which the US is a vestige.
Jesus never told us to fix the Roman empire, and Paul certainly never took that as his mission. There is no indication that the early Church fathers of the 2nd and third centuries ever took up the mission of fixing the Roman empire.
After Constantine and the next two emperors made Christianity the Roman state religion, people got the idea that they
could make pagans obey God by putting a sword to their throats, and that's where Christianity was headed up unto the Protestant Reformation into the Thirty Years War. That ended the future possibility of a Holy Roman Empire, but kings still considered it their right to dictate the religion of their subjects (as kings had been doing since Nimrod).
Because the king was the patron of the Church, the Church had a stake in the king's success, whether it was by holy or unholy means. Because the king gave status to the Church, it was socially advantageous for ambitious men to profess Christianity and take Church leadership positions whether they truly believed it or not.
But a number of theologians realized that the historical mingling of church and king--the use of the king's sword by the Church to enforce Christianity and the use of the Church by the king to give moral justification to his actions-- was inherently detrimental to holiness. The believed that in order for the Church to remain holy, it must be kept separate from the State. Those people were called "Separatists," which included the Pilgrims and Puritans.
Between the time the Pilgrims settled in America and the American Revolution, the English Civil War--a war between the Separatists and those who believed in the "Established Church"--had occurred, which solidified the concept of the separation of Church and State in the American colonies.
Roger Williams--the Puritan pastor who founded the first Baptist congregation in America--was also the first to coin and use the phrase, "wall of separation between the garden of the church and the wilderness of the world" in his 1644 landmark treatise "The Bloudy Tenent of Persecution for the Sake of Conscience."
It's no coincidence that
Baptist doctrine still concisely enunciates the proposition: