I mean specifically, what rights, privileges, qualities and situations in America did NOT derive from Christianity?
Here's just a small taste that I think answers your question: First. Baseball doesn't derive from Christianity. And I like the fact that we have baseball. Further... I like the fact that we don't let the religious have a special say or privileged place in the structure of our society. I like the fact that if people want to be immoral or sinful in a way that does not breach secular law that the Christians can't convene religious courts to punish that sin. I like the fact that people have the freedom to purchase pornography or if they wish. I like the fact that people are free to believe, say and proselytize that there is no God, that Jesus never existed, or that their particular god or gods should be worshiped. I like the fact that the law will punish any Christian who tries to officially retaliate against the person who says there is no God. I like the fact that the law will punish any Christian who abuses his position and tries to use public money, public settings or public laws to further Christianity. I like the fact that we've embraced pre-Christian aspects of Western Culture, such as democracy and republicanism. I like the fact that people are not required to honor their father and mother or covet their neighbor's goods. I like the fact that there has been a lessening of first Protestant bigotry, then Christian bigotry, now religious bigotry in official American life. I like the fact that scientific progress isn't held back by the rantings of biblical literalists. I like the fact that one doesn't have to be bothered by you "respecting the Sabbath," if he himself doesn't wish to. I like the fact that Americans are free to manufacture and worship idols. I like the fact that a Muslim, or agnostic, or Sikh, or Buddhist or atheist or a Wiccan or Shintoist, upon merely holding a belief in American political philosophy and achievement of citizenship, can be as American as the descendants of the very first Protestant Christians. I like the fact that America, from early on made it known to the world that we are not a Christian nation. Basically, I like the fact that I am permitted in America to live my life in the manner of my own choosing and not have to worry about some self-righteous pig giving me crap because the way I choose to live my life differs from what he believes his "god" requires.