The denial is frequently accompanied by a contrast between the decadent secularized United States and the theocratic nation-state of ancient Israel.
However, one can imagine a pious Israelite saying the same thing about ancient Israel. He could argue that Israel was never a religious state, or Jewish state. He could point out that most of his contemporaries are nominal Jews. Many of them dabble in the occult. Ape the idolatries of their pagan neighbors. Are morally corrupt.
For that matter, you could just as well deny that the church either is or ever was a Christian body. The church has always been a mixed multitude. The faithful few have always been…few.
Then you have Nietzsche’s quip that “The last Christian died on the cross.”
I’m not claiming that America is a Christian nation. Rather, I’m pointing out that the criteria used to deny the Christian identity of the US are so utopian that nothing short of the new Jerusalem would pass the test. If perfectionism is the standard, isn’t that pretty vacuous?