I have heard that interference from Moscow has been the cause of some dissent and even a schism within the Russian Orthodox Church in America. I think the very existence of the Russian Orthodox Autonomous Church of America is proof positive that at the least there was once an issue with control from the state.
Are the various branches of Eastern Orthodoxy (e.g. Greek, Russian, etc) independent today or are there are still ties to the respective states?
The commingling of states with Orthodoxy is a recent (19th century) historical phenomenon known as phyletism, and has to do with the rise of nationalism. This is why you see Macedonian, Greek, Russian, etc. Orthodox churches. Patrick J. Deneen explains how nationalism became a prominent ideology in western culture:
“[There is] an impulse that can be dated back to the beginnings of the modern era and the rise of the state. Before the latter’s ascent, memberships in various social settings were overlapping and varied, ranging from families, neighborhoods, townships, boroughs, regions, guilds, Church (parish and Catholic), nation, even empire.
The state undermined competing allegiances by demanding primary allegiance to itself alone, and only secondarily and ‘voluntarily’ to these preexisting institutions. Such memberships became less and less ‘constitutive.’ Rather, such associations and memberships came to be viewed as secondary to our primary allegiance to a State that reserves the right to control, oversee, and define any other institution….
The only liberty that could be recognized was the liberty of individuals to ‘pursue his or her own ends.’ The ancient rights, privileges, immunities and liberties of institutions—the Church, universities, guilds, localities—were redescribed as forms of oppression. The increased power, even intrusiveness, of the state, was justified not as a form of oppression, but rather in the name of liberation of the individual….
During the bloody twentieth century, the Church stood against the totalitarian ambitions of Fascism and Communism. A third ideology is clearly flexing its muscles today—threatening to make those victories of the last century merely Pyrrhic. The totalitarian impulse today is embedded in the very logic of liberalism, which seeks to expand its dominion into every aspect of life and against every competitor to its demand for the exclusive allegiance of individuals. We need to keep firmly in mind the picture that adorns the Leviathan, and resist our absorption as individuals into the body of the state by retaining deep, abiding, and even primary allegiance to family, locality, and Church.”
Phyletism is a confusion between church and nation, and was officially condemned by the Ecumenical Patriarch in 1872 (yet the practice still remains and is one of Orthodoxy's main problems).
Despite differing national affiliations, Eastern Orthodox Christians are members of one Church and share the Orthodox faith. These affiliations indicate what language and ecclesiastic jurisdiction the church falls under, but they are still considered to be members of the Eastern Orthodox Church. The respective governments of these nations are not necessarily in charge of these churches, rather they fall under a bishop in that country. Another question on C.SE explains further that Orthodox Christians of different ethnic affiliations share the same faith.
At least in Russia, the Czars had pretty well taken over control of the Church by the time of Ivan the Terrible, replacing their Patriarch with an Oberprocurater, or attache of the Czar to rule over the government of the Church. It would seem that the Current Russian Government seeks a return of this form of Church nationalism. As to whether this is a good or bad development, I am not sure. The notion of separate independent churches doing their own thing under the shadow of the Secular arm does not seem to last for long as an alternative.
