To say that the three Abrahamic religions are "all the same thing" is incorrect: in practice, in history, and in eschatology.
It's obvious what you wanted to happen here. You throw out bait asking for a Christian to back up the widespread assertion that America was founded on Christian principles, some Christmas/Easter Christian shows up and rants how this is a Christian nation and that we've strayed too far, and then you bust out about how these "Christian principles" are really just innate moralities that were put into practice long before the Ten Commandments were obtained, the Bible was written, or the Constitution was drafted. Everyone is supposed to be in awe of this previously unknown historical tidbit, and happily converts to atheism. Checkpoint for evangelical atheists and Richard Dawkins.
But American isn't and never was a Christian nation. It's all a myth. American was founded by religious dissidents (Massachusetts) and economical opportunists (Virginia). Our government was crafted by 18th century liberal Enlightened thinkers. Along with westward expansion (see Turner's thesis), that's America. That's all it is. Everything you are so passionate against (public prayer, the war against gays, etc.) isn't even Christianity, but rather a corrupted American civil religion reinforced by lazy Americans and opportunistic right wing politicians and talking heads.
If you want to know what Christian principles are, read the "Sermon on the Mount". That passage pretty much sums it up. Anything you see that doesn't mesh with that IS NOT CHRISTIAN. It's really not that complicated.