The idea of separation of Church and State came from the Reformation, and it was explicitly about separation of the legal entities. And they were legal entities - notably under Calvin the Genevan Consistory was the entity in charge of religious life and it was separated to the civil authorities.
You've misunderstood your own sources. The Lutheran doctrine of two kingdoms, according to which the church is not a legal entity but which exists in the spiritual kingdom, was a way to protect the church from the law and other secular authorities. This doctrine was then adopted by Calvinists, one way of which is the way that you're talking about.
> this has nothing to do with consent laws, which are entirely a matter for the state.
That's what I've been saying. And it has nothing to do with my point.
See
https://en.wikipedia.org/wiki/Two_kingdoms_doctrine#Response...
https://en.wikipedia.org/wiki/Genevan_Consistory
In any case, this has nothing to do with consent laws, which are entirely a matter for the state.