If most of the founding fathers were strictly against the combination of church and state, when how did the state and the church become so intertwined?
While it's not an answer, it's useful to put "separation of church and state" into the context of the time.
Most European nations at the time had a state church or an official religion. England had (and still has) the protestant Church of England. France and Spain both held to the Vatican, and the Netherlands to the Dutch Reformed Church.
So when the Bill of Rights gives us "Congress shall make no law respecting an establishment of religion" they're preventing the establishment of a state church in the US.
To this end, "the church" and the state never did become intertwined. While it's arguable that Christianity does punch above its weight within the federal government, there's no one church that can be seen to be pulling the strings (compared to, eg, the Roman Catholic in Ireland, or BOR in Romania).
A lot of Christian denominations and groups were seeking religious freedom from the established churches in Europe. The Presbyterians in Scotland and the Puritans in England were actually all about overthrowing the Church of England. When their revolts were thwarted, many sought refuge in the wilderness of the New World. This was well before the Enlightenment period of the 18th Century that influenced the ideologies of the US founding fathers.
As to the separation of Church and State debate, that finds it's home in the conflict between Enlightenment thinking and the idea that everyone in a society automatically belonged to the Church and fell under Church moral authority which was so prevalent during the previous millennia.