What's most important under American Federal Law? Life, liberty, and the pursuit of happiness.
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
I think this gets to the crux of it. There are two streams in Protestantism. One is self-aggrandising and pleasure-seeking, the other is self-debasing and self-destructive. The US was built on the former. It doesn't matter whether the source is Baptist, Quaker, Masonic or otherwise, the guiding spirit is mostly pride and pleasuredise
The Orthodox Church should be orthodox and universal. The Catholic Church removed the orthodox element, an inserted a man to divine truth. Then the Protestants removed the catholic (universal) attribute from the church, which quickly led to the idea that everyone can divine truth, when truth has already been given to us by God

. The Catholic church is still universal, in that it's all under one man. Protestants don't even bother to come up with a narrative that their religions are divine, or that their guy has a direct line to God. At least a church like the the LDS say they are representatives of divine revelations; though I believe they have men divining within the church too.
The natural response to coming out of the church of God is to do as Eve did, seek pleasure and riches that you've just been warned about. That's what the founders were doing, and many before them. Most of the founders believed in petty aristocracy. Only 6% of people/men (I forget) were able to vote. Their franchise inevitably had to be extended until the above quote could be said to be about as true as possible.
Once you hit maximum pleasure and joy, the progression is into pestilence and misery. Our ancestors were blinded by the lights of the world, so that most of us have no way to countenance materialism by jealousy, anger and despondency. This has been rapidly growing in the culture over the past 10 years in particular, but it's been growing for 100s of years. But we are now living in a time when those impulses are stronger, and seeking to burn down the shining city on a hill, your tower of Babel. Universities are primarily factories to produce such people.
If you go into churches in America, you will typically see people trapped in joy or scolding themselves in flagellation. Both have no place in the history of the church. They were adopted by men. The flagellators have deluded themselves into thinking the path to God is via self-destruction along a road of guilt. When God taught us to seek true repentance and thus forgiveness, rather than carrying these burdens. Those seeking joy are deluded into thinking that the path to God is a one filled with endless dopamine hits and engorgement. When God taught us to be humble.
I think the history of Christianity in the US is of those two streams, with the culture that is gifted by Christianity constantly evaporating. The culture remains as a residue by inertia. How much of Christ was left at various points is hard to say.
Recently a self described "soft-lib" was talking to me about Christianity. He is not a Christian, but sees something there, an element that is missing. Naturally he has no understanding of orthodox Christianity. He thinks more religion would be better, but it should just be something that is in the corner. A nice little place of warm and cosy feelz. But that place should have no real bearing on society.
Christianity is a church, if you can keep it. We couldn't keep it.
America is a republic, if you can keep it. You couldn't keep it.
The last days are a clue, if you can recognise it.
the experiences of English people in schools and it seems many of them still receive religious education
I don't know what it's like now, but when I was in school, we had at least one weekly assembly with a priest from The Church of England. There were two. One was professionally boring. The other was very energetic and positive. He had quite a big effect on me. Although I didn't consider myself a Christian or believe in God at the time. As a young child I also went to a Methodist nursery. I remember specifically believing in God at that time. But I think that ended at age 5 when I went to normal school and Christianity was just one thing that was there, in the same way that maths was there. I also remember another guy who came in once who was also very positive and proactive. He was telling us about Barabbas. He and the priest I liked had a very evangelical element to them. I am now very suspect of that behaviour, but not really sure why. But I feel evangelical proselytising to be very disingenuous and coming from an unhealthy place that I don't know.
Anyway, I had some cues in life to predispose me to being self-debasing, self-sacrificial etc. And the CoE, being a self-debasing organisation, feed into that. So my idea of Christianity, was essentially hurting yourself to show you are good. This is a grad perversion and one of the biggest of our time. You will all probably be familiar with The Guardian newspaper. This came from the stream of Methodism, which was even more self-debasing than the CoE. Their endless insanity with things like getting a vasectomy to save the planet, mass immigration as a punishment for colonialism etc. has all come from the wreckage of Godless Christian denominations. They don't do these things because they are good, but because they are given over to Satan.
Later I went to a private school that had it's own chapel. But it was just boring, and no one paid any attention to it. But it's slightly better than it not being there at all. It's a thread that one can unravel.
Just reading, it appears that this is not surprisingly slowly devolving into generic or multi-faith setups. Further reading shows the general trend in Europe:
1800s - Christian schools created by churches
early 1900s - state takes control of Christian schools under the understanding they will continue to by explicitly Christian
around the 70s - schools are no longer explicitly Christian
around the 80s - religious education (a class) is introduced
more recently - religious education become - religious, philosophical and ethical studies
about now and the future - religious education is replaced with civic and moral studies
France has replaced it with
éducation civique et morale. In the UK, when I was in school there was something called PHSE (Personal, social, health and economic education). I would guess that will replace religious education. I remember in this class they were teaching us about usury - mortgages. I remember asking a question how they can do all this money changing, sensing what I found out next year was fractional-reserve banking. Obviously the teacher had no idea about this. I asked a similar question when learning about the great depression. How could there have been a run on banks? Unless they didn't have the money. I guess I've always had the spirit of a troublesome goy in me with these inconvenient questions. If I was to describe my time in school I could do it with one word - gay. And PHSE was the gayest part.