I'll give the Conservative Christians their pet mantra: The United States of American was founded according to Christian principles as one nation under God.
However, it should also be admitted there were a variety of competing denominations, each mistrustful of what the others would do should they become the Official state-approved Christianity.
In the USA secularism results from Christian denominations competing with one another. They all want(ed) to be the Official Church, but the reality was that none of them could achieve supremacy.
When I covered the Federalist Papers and The Constitution in the US History class that I taught once upon at time, I summed up Federalist #10 this way: the cure for faction is more faction. Just for the record, when reading No. 10, substitute "special interest" and "lobbyists" for "faction."
I bring up No. 10 because in it Madison shows how plurality is the guarantee of freedom and constitutional stability. Any of the Protestant denominations unchecked by the others would give Calvin's Geneva a run for it's money. BUT sometimes they make common cause to achieve something some or even all value.
A less charitable rephrasing: separation of Church and State protects Christians from themselves. Once the machinery for maintenance of doctrinal purity is set in motion, it is very, very difficult to be gotten rid of. New heresies and new sinners can always be found. And besides, what would all those out work bureaucrats do? Payroll size and budgets are very much the measure of administrative ego and power.