Fine with me, with respect to matters of religion, so long as you mean it all the way. But don’t go telling me that it’s bad for the Federal government to interfere in such matters, but perfectly OK for local governments to do so.
If a teacher comes into my (hypothetical) child’s classroom and leads the kids in prayer, that teacher is a government agent, and is telling my kid what to do, in a matter of no direct relevance to the education she’s supposed to be providing. Ditto if she tells one of the other kids to get up and lead a prayer, or demands the class’s attention when a classmate spontaneously gets up and begins praying.
The Bill of Rights exists, in large part, to keep government off our backs in ways such as this. If you like, it’s one part of government (the Constitution, interpreted by the courts) acting to keep another part of government (whether Federal, state, or local) from interfering with your business and mine - in this case, the religious education of our children.
BTW, while the phrase “separation of church and state” is a descriptive phrase of Jefferson’s, most everything it describes can be found in the Establishment and Free Exercise Clauses of the First Amendment. In this case, for instance, for the teacher to expose my child to prayers I hadn’t approved of interferes with my free exercise of my faith - which includes my right to give my child the religious upbringing I choose, without anyone else’s interference, especially the government’s.
And to the extent that those prayers support one religious point of view over another (including the absence of belief in a deity), the government would be acting to give that religious point of view a privileged status. That’s ‘establishment of religion’.
Nobody’s impartial about religion. I’m certainly not. Noggin, you’d probably not want me teaching your kids about what it means to be a Christian, and I certainly wouldn’t want you teaching my kids about it. I’ll teach 'em myself, and take them to a church of my choosing. But I don’t want a bunch of people whose religious judgment I don’t trust, or their kids, being given a leg up by government to teach my child what Christianity is supposedly about.
And that’s from a fellow Christian. I’m sure practitioners of other faiths, and atheists, feel just as strongly on this issue. The schools are theirs, too, and they have every right to trust that those schools won’t be used to teach their kids about religion in a way that bothers them.