Yes the Church and State need to be separated – from each other. Ultimately they still come under God’s authority, take a moment to read an excerpt from "Box Theology"
In the modern world, the humanistic state claims this sovereignty: it is the modern god walking upon earth.-The modern state claims sovereignty and catholicity; the United Nations is the attempt of humanistic statism to attain true and full universality and catholicity.
Meanwhile, the Christian Church is busily departing from the doctrine of God's sovereignty and His necessary catholic jurisdiction. Christianity is increasingly limited to a "spiritual" realm (of which it now concedes vast areas to. psychology and psychiatry), and the rest of the world is granted to the state.
The result is box theology. To understand what box theology is, let us compare the universe to the Empire State Building, a great, modern, skyscraper office building. In box theology, the church claims one small office among hundreds for Christianity. All the rest of the building is given over to the jurisdiction of the state and the sciences. One area after another is deemed non-religious and is surrendered. This is done despite the fact that God is the Creator and Lord of the whole universe and therefore has total and absolute jurisdiction over all things. God's law-word, jurisdiction, and authority must govern all things. "All things were made by him; and without him was not any thing made that was made" John 1:3).
The jurisdiction of the church is a limited one, but the jurisdiction of the triune God, of Christ our King, and of the Bible, God's law-word, cannot be limited. Every area of life and thought must be under the dominion of the Lord: He alone is truly sovereign. To limit the jurisdiction of Christ is to posit a limited god, one who cannot survive because a limited god is a contradiction and is no god at all. If God is God, if He truly is the Lord or Sovereign, everything must serve Him and be under His dominion, the state, schools, arts, sciences, the church, and all things else. To limit the jurisdiction of the God of Scripture to the soul of man and to the church is to deny Him. A limited god cannot save man, because he is not in control of all things; what he does today can be undone tomorrow, and his "salvation" is at best temporary.
However even if they are separated it does not prevent either institution (Church or State) from speaking out when the lines of jurisdictional authority are crossed. Why was there a profound silence from church leaders when the state crossed the line and stepped into the jurisdiction of parental authority? Why do churches apply for an exemption from tax when the state has no authority to tax what is given to God’s church for His work on this planet? These are questions that need to be answered and addressed – from the pulpit and from God’s Word.