I feel like they should have way more leeway than that considering how Armenia is one of the more well-integrated regions of the Empire politically and culturally speaking. There were many Emperors within the Empire's history of Armenian origin after all. The Macedonian dynasty originates with Basil I who was an Armenian peasant. Though I think Constantine VII tried to smooth out his grandfather's pedigree by claiming some distant relation to Armenian nobility.
So rather than really second class citizens there should rather be some more minor stigma towards the Armenian Church kind of like how in the German Empire there was a little bit of tension between the more Protestant North and Catholic South. Both were still German citizens though.
You're comparing apples and oranges here. You say there was only a little bit of tension in Germany but that was only because of the existence of nationalism. We are two hundred years before that.
Before then some of the most destructive Wars in European history until Napoleon were fought between North and South Germany. Until the age of nationalism based on nationhood, race, or secular citizenship comes around the current community organization of the European world is via the church. Just look at how Anglicans and Puritans were treated during the course of the English Civil War, as well as other Protestants like the Scottish Church in the Bishops' War. Or one of the many French Wars of religion, the eighty Years War, or any other one of a litany of conflicts from this century all based around religion.
It makes absolutely perfect sense that people who do not describe to the state's chosen ideology, that being the Greek Orthodox Church, are not treated very well.