What fact factory pumped you that load of bullshit? Government enforced religion is what they were fleeing from. They wanted to worship God according to their own conscience, not one dictated by law. All State constitutional religious freedom clauses state that the State cannot establish religion or support a particular religious sect, such as the Church of England being imposed as an official religion. Religion free from government.

If you think they wanted God out of government, then why is it that in every State current constitution's preamble is a directly statement of a gratefulness to Almighty God or invoking God's favor? Some States even attribute all CIVIL and natural RIGHTS or LIBRTY as coming from God. The few States that do not have a preamble all at least acknowledge Almighty God, the Supreme Ruler, the Supreme Ruler of the Universe, our Creator, etc. in a religious freedom clause, except for New Hampshire which does at least refer to God. None of them refer to a God, ostensibly inferring a belief that there is only one God.

Hell look at Vermont's Religious Freedom clause

That all persons have a natural and unalienable right, to worship Almighty God, according to the dictates of their own consciences and understandings, as in their opinion shall be regulated by the word of God; and that no person ought to, or of right can be compelled to attend any religious worship, or erect or support any place of worship, or maintain any minister, contrary to the dictates of conscience, nor can any person be justly deprived or abridged of any civil right as a citizen, on account of religious sentiments, or peculiar mode of religious worship; and that no authority can, or ought to be vested in, or assumed by, any power whatever, that shall in any case interfere with, or in any manner control the rights of conscience, in the free exercise of religious worship. Nevertheless, every sect or denomination of Christians ought to observe the Sabbath or Lord's day, and keep up some sort of religious worship, which to them shall seem most agreeable to the revealed will of God.