The idea that they should be congruent has a long history, as this article from Wikipedia notes.
Symphonia (Greek: συμφωνία “accord”) is a concept (theory) in Eastern Orthodox Christian theological and political thinking, which posits that church and state are to be complementary and exhibit mutual respect.
The theory can be traced back to Roman Emperor Constantine the Great (324-337). Justinian I expressed this position when he said: “A distinction is drawn between the imperial authority and the priesthood, the former being concerned with human affairs and the latter with things divine; the two are regarded as closely interdependent, but, at least in theory, neither is subordinated to the other.” Such a position is scripturally based as evidenced in several Old Testament texts; the most notable references being that of Melchizedek the priest-king and the brotherly relationship between Aaron, the high priest, and Moses, the leader of Israel from Egypt.
The theory is believed to have been embodied in the Byzantine Empire, where ecclesiastical and civil law were indivisible (the ecclesiastical laws were enacted by the emperor). It was reasserted in the Stoglav, a church code promulgated in the Tsardom of Russia in 1551. In Stanley Harakas’ view, “there are almost no existing presuppositions for its implementation as a system of Church-state relations in our times”, and “at most, it presents ‘an impossible ideal’ in the contemporary world, which may illumine some attitudes for Orthodox Christians regarding their views of the well-ordered state as well as the relationship of the Church toward the state.”
The Symphonia theory became the subject of political discussion in Russia when it was brought up and dwelt upon by Patriarch Kirill of Moscow in President Dmitry Medvedev‘s presence the next day after Kirill’s accession to the Patriarchal throne on February 1, 2009.
Retrieved January 3, 2015 from http://en.wikipedia.org/wiki/Symphonia_%28theology%29