But my priest told me that I could be an anarchist AND Orthodox at the same time...
That's because you're a Holy Fool. You serve the God-Appointed Emperor by pointing out his extremely few errors and excesses. You are the schizophrenic backbone of Justinian's symphonia
Your first task as Holy Fool is to dress in sackcloth and ashes, and beat your breast in front of your local courthouse or capitol building. You may cease as soon as the president resigns and an Orthodox leader replaces him, thus putting an end to the Time of Troubles.