I don't know when government began the funding or regulation of public schools, but I know as sure as I'm sitting here that lessons in Christianity were taught in our schools in the very early 1800's. I've seen, read, and sold the books.
Judging from your reply to me I know you'd be astonished to learn just how much the Christian faith was integrated into the teaching in American schools of morals and values. I'm not saying that any specific denomination of Christianity was taught in schools, but what they did was take a lesson in morality or character from the Bible and put it amongst other lessons from secular history to teach American children how to behave in society. This stuff was as common as the gray squirrel.
The original McGuffey Readers, published in the mid-1830s, were unabashedly Protestant. The second edition, published in the 1870s, was less religious (probably because of the influx of Roman Catholics into the US) but still moralistic. They were in use until 1920s.
I think you've misjudged me. To address your concerns, I'm not upset about the Christian content in early American schools. I was questioning Jefferson's (that is, the federal government's) involvement.