It is the belief of this student that when one understands the meaning of ἐκκλησίᾳ and the history of the church/state relationship he will understand the beauty of Christ’s design for His church. He created the church to be in the world but not to be conformed by the world. He created His church to be an assembly of believers who encourage one another toward obedience to His commands. As such, it is the belief of this student that the church (as an assembly local or universal) does not have a social responsibility whatsoever. However, there is a Christian responsibility to love God and others, and this responsibility falls upon the individual.
If you would like to look into this topic some more. Look into the books below, which I found imminently helpful.
Balz, Horst Robert, and Gerhard Schneider. Exegetical Dictionary of the New Testament. Grand Rapids: Eerdmans, 1990.
Barnett, Paul. The Birth of Christianity: The First Twenty Years. Grand Rapids: Eerdmans, 2005.
Bauer, Walter. A Greek-English Lexicon of the New Testament and Other Early Christian Literature. Edited by Frederick W Danker. Chicago: University of Chicago Press, 2000.
Bennison Jr., Charles E. “What Does it Mean to be a Church in an Age of Massive Hunger?” Anglican Theological Review 61/3 (1979): 316–330.
Bloesch, Donald G. The Church: Sacraments, Worship, Ministry, Mission. Downers Grove: Intervarsity Press, 2006.
Bock, Darrell L. A Theology of Luke and Acts: Biblical Theology of the New Testament. Edited by Andreas J Köstenberger. Grand Rapids: Zondervan, 2012.
Brown, Colin, ed. New International Dictionary of New Testament Theology. Grand Rapids: Zondervan, 1986.
Carson, D. A. Exegetical Fallacies. 2nd ed. Grand Rapids: Baker, 1996.
Davidson, Ivor J, and David F Wright. A Public Faith: From Constantine to the Medieval World: AD 312-600. Edited by John D Woodbridge. Grand Rapids: Baker, 2005.
Ferguson, Everett. Church History, Volume One: From Christ to Pre-Reformation: The Rise and Growth of the Church in Its Cultural, Intellectual, and Political Context. Grand Rapids: Zondervan, 2005.
Grudem, Wayne A. Politics According to the Bible: A Comprehensive Resource for Understanding Modern Political Issues in Light of Scripture. Grand Rapids: Zondervan, 2010.
Hammett, John S. Biblical Foundations for Baptist Churches: A Contemporary Ecclesiology. Grand Rapids: Kregel Publications, 2005.
Hauerwas, Stanley, and Samuel Wells, eds. The Blackwell Companion to Christian Ethics. 2nd ed. Oxford: Wile-Blackwell, 2011.
Hayes, Edward L. The Church: The Body of Christ in the World of Today. Edited by Charles R Swindoll. Swindoll Leadership Library. Nashville: Word Publishing, 1999.
Husbands, Mark, and Daniel J Treier, eds. The Community of the Word: Toward an Evangelical Ecclesiology. Downers Grove: InterVarsity Press, 2005.
Kunst, Theo J. W. “The Kingdom of God and Social Justice.” Bibliotheca Sacra 140 (1983): 108–116.
MacArthur, John. Why Government Can’t Save you. Nashville: Word Publishing, 2000.
Mueller, William A. Church and State in Luther and Calvin: A Comparative Study. Nashville: Broadman Press, 1954.
Pierson, Paul E. “Local Churches in Mission: What’s Behind the Impatience with Traditional Mission Agencies?” International Bulletin of Missionary Research, 1998.
Ryan, E. A. “Three Early Treatises on the Church.” Theological Studies 5/2 (1944):113–140.
Smith, Gary Scott, ed. God and Politics: Four Views on the Reformation of Civil Government: Theonomy, Principled Pluralism, Christian America, National Confessionalism. Phillipsburg: Presbyterian and Reformed, 1989.
Verduin, Leonard. The Anatomy of a Hybrid: A Study in Church-State Relationships. Grand Rapids: Eerdmans, 1976.
Woodbridge, John D, David F Wroght, and Ivor J Davidson. The Birth of the Church: From Jesus to Constantine (AD 30-312). Vol. 1. The Baker History of the Church. Grand Rapids: Baker Books, 2004.
Young, Doyle L. “What Difference Does it Make, Anyway? The Priesthood of All Christians Applied to the Local Church.” Southwest Journal of Theology 30, no. 2 (1988): 46–54.