My interviewing hasn't worked out so far to find out how Sunday school was in earlier times. So we'll move on....
So by the time I was born it was understood that schools had the responsibility to teach academics and Sunday schools had the responsibility of religious training. Now two major things have happened to change this arrangement somewhat.
First of all, public schools do not include religious undertones at all. Fifty years ago, schools might have even read from the Bible to begin the school day. The Lord's Prayer and the 10 Commandments could be found on classroom walls.* When I was in elementary school around 1977, we began our day with the pledge of allegiance, a patriotic song, and a "moment of silence." This was done school wide on the P.A. system. When I was a teacher the moment of silence was gone. So, where as Sunday schools began as a means of teaching poor children how to read, using the Bible.....today's public school is still charged with teaching, but without any religious means of doing so.
And here is where, apparently, private Christian schools and homeschooling began to really come into play. Parents who wished to have their children's education NOT be separated from their religious education began looking at these choices more and more. Ironically, what began as a mission for poor children now did not serve them at all. Poor children have been left to the public school alone.
Next....the second change.