The doctrine of the Church is related to such important issues as the worship of God, the administration and meaning of the sacraments, salvation, sanctification, evangelism, marriage, family life, vocation, politics, economics and sociology. Meanwhile, the doctrine of "Render unto Ceasar" is related to secular issues such as the administration of law (marriage and family life included), politics, economics and sociology -- secular matters that religion makes a business of and interferes with; but has no business being in.
Your absolutly right. That why we should have a seperation of church and state.