It amazes me that the separation of church and state is contradicted more in breach than compliance.
State essentially means the people of common destiny united and organized for security, peace and common interest: the common good. It is intrinsically based in and arises from the increasingly complex relationships of people in common and between states. Of course is makes sense for these processes to be informed by the interests and acumen of religion. Of course it is reasonable to see conflict. 
The real challenge of state is how the pursuit of the common good is determined and how inevitable variations of views are resolved rather than devolving into conflict.
If there is a "natural" expertise in "natural law" it is, or should be, the state. (We Christians should have confidence/"faith" in this as we are "in the image and likeness of God". Shhhhh...)
Church violates natural law by dogmatism & pretense of member representation
State violates its "common good" by dogmatic religiosity.