True, Baptists have come a long way from the beginnings in England, where they were beaten and imprisoned by the church-state that produced the KJV Bible, and in America where the dominant church did them the same way, depending on the particular colony or location. So they were "free church in a free state" pioneers, and stood by that through the Revolution, and the gradual elimination of state-established churches like Congregationalists in Massachusetts and Connecticutt. But in the public school movement, which began in the mid-19th century, I don't see that they opposed using the Bible as a major textbook, or prayer to begin the day. Catholics, growing in numbers, did of course oppose Protestant prayers and Bible readings, so the Baptists also opposed using public funds for exclusively Catholic schools. It seems to be in that context where Baptists had begun to view a complete separation of religion from all government entities meaning that their children would not have their values reinforced in their children's formal learning-- remember something about It takes a Village?
So public schools are 'where it's at' in the minds of Baptists, as well as most everyone else, in shaping the meaning of 'separation of church and state.' Is teaching devoid of God godless? By definiation, yes. And, of course, there is the debate about what the Constitution really says and requires. The 1st Amendment certainly has not always meant that the states could give no privileged position to a religious view or institution, as some still retained established churches well into the 19th century. But it was only in the mid-20th century that the 14th Amendment and its "equal protection" clause was used to force any state action into the category of the 1st Amendment's "Congress shall make no law..." equivalency.
By the time I went to school there was no more prayer or Bible reading in class, but there was prayer before football games and at graduations, and I remember the P.T.A. invited local ministers to deliver a devotional at their monthly meetings. Baptists were certainly involved in these things, and this was years before what they call the "conservative takeover" of the SBC. So I think the issue is not as polar as it if often made out to be.