This is a great question, one that is at the center of a lot of "church and state" debates these days. Based on the quotes you provided, mainly from Thomas Jefferson, you are certainly making the point that some of the founding fathers weren't Christians in the most accurate of the word. By definition, a "Christian" is someone who is a follower of Jesus Christ.

In the the book of Acts, which is the historical record of the early church, the disciples (followers) of Jesus Christ were first called Christians at Antioch (Acts 11:26). And who were these Christians? They were those "who had been scattered by the persecution in connection with Stephen" (Acts 11:19), and some from Cyprus and Cyrene who told Jews and Greeks "the good news about the Lord Jesus" (Acts 11:20). The result of their witness was that "a great number of people believed and turned to the Lord" (Acts 11:21).

What was true in the first century was true in the 18th century when America was founded, and it's true today. A Christian is someone who believes by faith in the person and work of Jesus Christ, and who turns (the Bible word is "repent") away from a life devoted to self to a life devoted to Christ.

Even belief in God does not make one a Christian. James the apostle wrote: "You believe that there is one God. Good! Even the demons believe that--and shudder" (James 2:19). James' point is that belief in God alone does not make a person a Christian.

As you point out in your quotes, Jefferson shuddered, not in belief in God, but in belief in Jesus Christ as God incarnate. Jefferson was so averse to Christ as the Son of God that he took a Bible and physically cut out any reference to the miracles and the divinity of Christ (this Bible is famously known as "The Jefferson Bible"). To Jefferson and perhaps many other founding fathers, Jesus was a good moral teacher, nothing more.

Well, Christianity is not about belief in a good moral teacher. It's about belief in Jesus as God in human form, who came to earth to seek and to save sinners (John 3:17, Luke 19:10).

So why do people think that America was founded as a Christian nation? Because they believe that anyone who believes in God is automatically a Christian. And since Jefferson, who was the principal author of the Declaration of Independence, evidently believed that God exists, people have just assumed that America was founded as a Christian nation.

By the way, if you're interested in reading a very thoughtful and well-written book on this subject, check out "The Myth of a Christian Nation" by Gregory Boyd.