I'm curious though - I know the state and the Church are fairly closely connected in Greece. Is that why they were involved in enforcing the change?
Everything you read on the issue is an oversimplification. There just the talking points and no side wants to really discuss the historical situation of Greece which lead to this problem.
From the time of WW1 to the greek civil war in the late 1940's the nation was bitterly divided over royalists and republicans. This was so severe that its known as the 'National Schism" in greek history books. There was so much political polarization that there was bitter fighting over calendars, over which form of the greek langage should be used, to what architecture pubic buildings should have.
The animosity and rift between the royalists and the Venezelists lead to the defeat of the greek army in Turkey which resulted in the Smyrna Genocide. During these early years (before and after Smyrna) everytime there was a regime change between the two factions they would also oust the archbishop and replace him with one loyal to their regime. So one archbishop would be exiled then brought back after the regime change, and once that regime fell again to their predecessor, the returning government would reinstate the former bishop while exiling the latter non-loyal one .
After the Smyrna catastrophe, the royalists who were in power during the fiasco were ousted once again. The new government came back to power and the church implemented the calendar change, this government is known as the Second Hellenic Republic and lasted from 1924-1935. The majority of the old calendarists tended to be royalists and heavy handed approaches were used to squash them. Some of the bishops of Greece either sided with the regime, while others were sympathetic to the old calendarists but kept silent not to draw the wrath of the regime.
By 1935 the pendulum began to swing the other way (an ongoing great depression and the absorption of 1.5 million refugees will do that) and the president became a royalist sympathizer. This allegiance change lead to the 1935 Venezelist coup to rid the government of royalists. The Venezelists were unsuccessful, the ywere crushed and the monarchy was reinstated. The venezelist sympathizers in the military were convicted of treason and put to death. There was a purge of the venezelists from the government. At that time, the bishops sympathetic to the old calendar felt free to return their diocese back to the old calendar without persecution.
This is how the old calendarists recieved there bishops. This is why the 1935 old calendarists declaration speaks of dividing the church between 'two opposing camps'. They reallly had in mind the National Schism, (though obviously sympathetic to the royalist position).
At that time there was a belief the old calendar would be returned as the bishops loyal to the previous government would either capitulate, be replaced, or whatever. Unfortunately WW2 came along and then the civil war broke out against the emergent communists and everything was put on the back burner. Thats how we went from there to here.