While the first immigrants to this continent were in fact Xtian, suggesting that the Pilgrims' et al belief system was the basis for the "foundation" of what would later become our nation would be like saying that the 13th century invasion of the Mongol hordes into Europe resulted in Poland being founded on "Mongolian ideals." Or that Scandinavian countries were founded on Viking pagan ideals.
Anyone who insists this country is founded on the Ten Commandments hasn't read the Ten Commandments (any of the multiple Biblical versions of them), or hasn’t compared them to our Constitution. Anyone who says that this country was founded on "Christian Values" (whatever they are) just needs to explain what "values" this country has that are defined in the Xtian bible that is unique to Xtianity and which have been codified in our laws.
Perhaps they will offer burning witches as a Xtian value. Certainly the Bible endorses that, and certainly thousands of colonists were killed as witches by Xtians. If so then absolutely that particular Xtian value was embraced in the 17th century by Xtians of this continent.
If enslavement and genocide of indigenous peoples is a Xtian ideal, then yes it too was widely practiced here.
If anti-Semitism and intolerance of other sects and religions, is a Xtian value, then indeed that value was embraced in the 17th century and forward by our early Xtian residents.
If trying to force people to honor the Xtian god by imposing blasphemy laws that fine, imprison or kill for their violation, then yes, that particular Xtian ideal was observed here as well.
Xtians may well stake their claim to those ideals and values. They are welcome to them. But nothing in our Constitution or in the Common Law (derived from pre-Xtian Anglo Saxon common law) speaks to Xtian "values" or infers any Xtian dogma, doctrine, or rituals. Freedom of speech is NOT a Xtian value. Nor is freedom of religion, nor the right to vote, nor granting private ownership of firearms, nor determining who is qualified to hold office, nor is the abolition of slavery, nor is the concept of equality. Jesus never spoke on these issues or endorsed them. And they sure weren't universally practiced in Christian Europe.
This country was a unique and bold experiment. It was founded upon rational thought, democratic principles, and our Founding Fathers’ explicit intent to avoid the “Christian ideals and values” that are the very antithesis of rationality and which enslaved Europe for nine-hundred years. For any person to say otherwise exposes them as deluded, an undereducated buffoon, a lying history revisionist or all of the above.