The Declaration of Independence, declared independence from England. In England, the King decided the official religion of England. The King formed the Church of England to be similar to the Catholic Church. However, the King added a divorce clause, so he could divorce his wife. The Catholic Church ddi not allow this. The King dumbed it down. Jefferson did not want a secular government to be in charge of religion, since this meant man will dictate to God, for man's own benefit. God was supposed to remain above man.
If Government was to decide which religion was to become nationalized, you end up with lawyers, politicians and their donors deciding the fate of God and Religion. Every bizarre left wing group would have addendum in the bible; polytheistic heathen religion.The idea was to let Religion remain organic, based on natural selection; free exercise instead of forced compliance to the whims of politics.
The best way to understand the position of Jefferson is to realize he did not come up with separation of church and state, in a vacuum. Rather our founding fathers, like Jefferson, built his ideas upon the thinking and experiences of his founding fathers. The founding fathers of Jefferson, among others, were the Pilgrims. They came to America to escape the state run religion of England, and its tendency to persecute anyone not with their program. The King used religion like a secular tool. The Pilgrim began with a socialist experiment, but found it necessary to change to free enterprise. Jefferson extrapolated from that.