While I’m on the subject of establishment:
A religious worldview will always undergird the state. This is inevitable. This is because a religious worldview will always undergird everything we do.
The problem in the past with church and state has been that a statist worldview, the belief that the power of the state can bring in an ideal society, has frequently masqueraded as a Christian worldview.
When the true Christian worldview undergirds a culture, then the state will be limited to only protecting public safety and safeguarding people’s lives and properties, because this is what God gave the state to do, in the covenant He made with Noah. They will do this in a way informed by the Christian worldview- again, this is inevitable.
What about the freedom of those without such a worldview? The Christian worldview is actually that worldview which is best suited to protect the liberty of conscience of those who are not Christians. This is precisely because the attempt to bring in the ideal society, which always ends up persecuting those who disagree with that worldview, is no part of the true Christian worldview. Jesus made clear that His kingdom is not of this world, else His servants would fight (just like the servants of all the other worldviews). Paul told us that the weapons of our warfare are not carnal. So while basic law and public safety will be provided according to a Christian worldview, there ought be no attempt to draft the power of the state to force agreement with the worldview.
So a Christian state can tolerate Muslims and atheists and others, as long as they are willing to live according to that state’s understanding of human rights, marriage, family, public safety and the like. And there will always be debates about the proper role of the state. But statism really should have no place in our thinking as Christians. People’s hearts and minds must be ruled by Christ; the state has no right to demand that allegiance.
The statist, on the other hand, aims for the creation of utopia, the perfect society, here and now, through the collected power of humanity, something the Christian faith rejects. Because the statists inevitably fail in this goal (because Christ is king), rather than realize their error, they always blame those who reject their worldview. This blame will always fall hardest on Christians, because all worldviews other than Christianity are essentially statist; they all look to the state in one way or another to create the ideal society. Christians alone simply reject all of the claims of the statist and look quietly for the hope of the Messiah. Because of that, they never go along with the statist program. This is why a modern progressive is more tolerant of a Muslim than a Christian. It might appear that a Christian has more in common, valuing human rights and liberty and the equality of women and the like, but the core value of the progressive is not any of these things. His core value is statism, and this he shares with the Muslim.
The materialist worldview that dominates the modern West is fundamentally statist, because if material existence is all there is, then our hope is only in this life, and therefore the greatest possible power must be harnessed to make this immediate existence as ideal and just and prosperous as possible. That greatest possible power is always the state, and the use of its power to create utopia is always oppressive and intolerant.
So I hold to something like a Christian libertarianism, with strong conservative tendencies. We should unabashedly champion Christian principles in matters of public policy, in those limited things which we believe the state should do, those things given to the state by God in Scripture (especially important here is recognizing the unique role that Israel played in God’s redemptive history and not trying to recreate that). We should reject utopian visions, which means engaging only slowly and cautiously in reforming or altering the institutions of the past. We should recognize that God alone is Lord of the conscience, and therefore the state should make no effort in advancing the Christian gospel or worldview; that is the job of the church. But the state should likewise make no apology for being a Christian state governed by a Christian worldview. Therefore the state should always ensure that the Christian church has a protected place in the culture, while officially favoring no particular Christian church over another.
If you are worried about religious freedom, the Christian worldview is the only one that actually protects religious freedom, simply because our hope is not in this world or this society, but in the age to come. The Christian state therefore can protect the religious freedom of others precisely because of this, in a way that no statist worldview ever can.