It’s not about the culture, it’s the fact that the separation isn’t actually really all of that separate. If you swap the “secular” elements enshrined in our government to another faith it becomes glaringly obvious that we are respecting an establishment of religion.

* One nation, under Allah, indivisible… (Islam)

* Marriage is a legal institution between one man any many women (Mormon)

* “The office is closed for Yom Kippur next Monday.” (Judaism)

* The right to bodily autonomy begin at birth so there is no moral issue with abortion (Satanic Temple)

Of course the people are descendants of protestants and so our customs would naturally reflect that but so does our government. As a country we were so concerned about escaping state sponsored religion that we didn’t stop to think at all about how codifying norms into law that come from a particular religion end up creating a religious rule in all but name. Like we don’t even pretend to have religious freedom in any meaningful sense — your right to practice the traditions of your faith or have your institutions respected ends where what is acceptable and normal as defined by Christians ends.