Separation of Church and State?

How does our notion of the separation of church and state stand up to Jer. 50:14 (and countless other places in the prophetic word)? Does the word of the Lord care what we think? Does it care what we've got enshrined in law? Consider also Jer. 51:5. Is the political arena neutral? Are not even the pagan politicians and potentates (and parliaments and congresses) held responsible to YHWH?