When a country separates church and state to the extent it's illegal to pray in schools, or post the 10 commandments, etc, then it ceases to be a Christian country and it has abandoned the Christian principles on which it was supposedly built!!
I think its worse when a country so abandons its teaching and understanding of its own history that it chooses to become willfully ignorant of the principles and sentiments of its founders and on which it was founded because it is more convenient and self-gratifying to imagine these principles as wholly consistent with their own.
To say that America was founded on Christian principles conveys such an incomplete understanding that it serves to mislead more than inform; it is similar to saying "meat comes from cows" as an argument against the inclusion of pork in your diet.
America was founded on principles that were not entirely Christian, theist, humanist, secular, idealistic, pragmatic, or even democratic. All of those adjectives can be used to describe the complex assortment of persons and ideaologies that worked towards the founding and influenced individual principles on which it was built. To characterize the founders, founding, or founding principles as a whole as any one of those things is wholly misleading as they were each individually many of those things and some of them are mutually exclusive but all present in their own ways. To characterize these principles and the founding as some lost ideal isn't any better as misrepresenting the diversity of influences.
Every time someone says "America was founded as a Christian nation" or "Our founding fathers were all secularist humanists" or "We should return to our founding principles" I am reminded how awful our education system is; the last notion is particularly ignorant. That we have moved away from principles of our founding to some degree is a very good thing in some non-trivial ways; practical things such as who could vote to the elitist anti-democratic views behind senators originally not being elected by those few who actually could vote.
Whether our government should behave more secularly or more theologically is not an argument settled by broad characterizations of its founding. Those that believe it is are generally either misinformed on our history or willfully misrepresent it. One may use the words and writings to indicate intent and principles that went into our legal foundations, but when one does this one realizes that reality does not provide the convenient and agreeable argument that historical-fantasies do.