First off, I always want to know which God we're invoking. Let's face it, among the various Christian denominations and non-Christian religions, there are all sorts of different views of God. Do we mean some "God" in general? (That would seem to be the idea that Thomas Jefferson, et al., certainly had.) The Jesus of the Bible? Allah? The life force of some other religion?
When someone says we have to put God back in schools or government, it's usually their god they want foisted into positions of power and influence.
After reading 1 Samuel 8, I'm not so sure that God is all that interested in those positions of power and influence, at least not the covenant God of Israel -- the one incarnate in Jesus Christ of Nazareth.
In most cases, it's the god whose job is to enforce and control our behavior so we'll act better, show more respect, and leave each other alone. Frankly, I wouldn't want my children exposed to the religious whims of one teacher or another. Kids go to school to learn how to read, write, and do arithmetic, learn geography, and so on, not to learn their morals and opinions from someone's conception of the Divine.
In short, I'm a Christian and I don't trust those positions of power and influence to invoke "god". Certainly not the God we Christians claim to follow in Jesus Christ. That God has a tendency of challenging political powers, not propping them up. Think the Exodus or the Cross.
Second, I'm a Christian, so I trust my sisters and brothers in the Church to teach our children in the faith. I trust us to pass on the "faith once delivered" and the prayers. But I don't trust agents of the state -- in whatever variety they might come -- to do that. Caesar, as Caesar, always has a lot of blood on his hands.
Usually, this argument is made in support of God in schools. But the Lord has invested the raising of children to parents and more broadly to the Church in baptism. Schools, especially public schools, have seen an increasing rise in their expansion of power in the education of children. And those powers have been encroaching on parental responsibilities for at least my lifetime. While it is surely a good thing when parents have communal help in raising children, it should never be that those social systems of support replace parents. Far more important than bringing God back into schools is getting parents back into their children's lives as the main source of their religious and moral formation, not to mention providing for their basic physical need.
See, my main complaint here is that it's not the job of American social institutions to proclaim the Gospel. That responsibility lies quite squarely on the shoulders of the Body of Christ. This, after all, was the primary reason that Baptists in early America were so resistant to giving any religious responsibilities over to the government. The center of the Christian faith is the proclamation of what God has done in Jesus Christ to reconcile the whole world back to Godself. It's not the government's job to deliver that message. That's why the Lord instituted the ministry of the Church and invested that ministry with the task of proclamation in preaching.
Schools are, by their very nature, institutions of the American legal system. While teachers can certainly exercise mercy when appropriate, their job is to teach and enforce rules, and guide children according to the grades and standards in place to measure their performance. In other words, in school, a child is evaluated on the basis of their merit and performance. That's not at all how things work in the Church. But it's a good way of doing things in the school.
When folks make cries like that made in the picture above, what they're really wanting is a return to a "simpler" time, when everything (everyone!) was in its "appropriate" place.
But here's the thing, the "good ole days" were never all that good.
The reason is we humans are a rather sinful lot. Just look at kids. (GK Chesterton once said that the only doctrine that had verifiable evidence was the sinful nature of humanity -- just by watching children.) When you let kids loose on the playground, you see it. Sin breaks out in recess. I know; I was a kid on the playground once. Bullies, cliques, poor performance, jealousy, fights, timeouts.
Instead of cries for more religion, why doesn't the Church step up and be more realistic about our teaching office responsibilities? About our prayers for the world in which we live? About our ministries to families, the poor, the imprisoned, the hungry?
Because I suspect as soon as we do these things, we'll find God is already at work in the very places we think we've excluded him.
As soon as you take Jesus seriously, you discover that he's not left out of any place. God in Christ can never be expelled from our schools or our government. Because God in Christ is reconciling all those folks back to himself.
We in the Church just need to be on the watch for that and join in where we see it.