It does not mean the child was born of Christian parents. The USA used to be a country that was saturated in Christian influenced culture. There are many people who hold no religious beliefs at all but are not against the practice of Christianity. The reason they would not send their kids to a Jewish or Muslim church is because the USA is neither a Muslim or Jewish nation, or at least was thought of that way in the past. America was synonymous with Christian culture. The thinking was that only Arabs send their kids to Muslim church and the Jewish church was exclusively for the Jewish ethnic group and both were thought to be foreign to the American way.
If you sent your kid to a Christian Church, it was for morality and you don't get your morality from unamerican cultures. I'm just saying that was the thinking.
It certainly was not exclusively for wanting your kids to believe a faith you had.
There are people who like a culture that was born in Christian influence but do not believe in the Christian God or any God.