They complained about Orthodox leaders being joined at the hip with the government. That's a long-standing problem with Eastern Orthodoxy; a side-effect of their doctrine of the nature of the state.
Something else that's of long standing is the tradition of the holy fool. From the article cited:
Indeed, the patron saint of holy fools is St. Simeon Salos of Emress. He retreated to the Syrian desert in the 6th century to devote his life to prayer, living on nothing but lentils. A few decades later, Simeon returned to town a completely different man. He tied a dead dog to his waist and entered town dragging the carcass. Simeon would throw nuts at the priests during worship services and publicly ate sausage on Good Friday. The seemingly nutty monk also helped people in the town, though never when someone else might notice and never taking credit. Simeon’s saintly deeds were done in secret. And no one could dispute that Simeon was very holy person, even the priests he pelted with nuts on Sunday. Simeon just poked fun at every attempt people made to feel themselves "holier than thou."
In Russian history the greatest of the "holy fools" was Basil the Blessed, a man so revered that the famous Cathedral in Moscow’s Red Square next to the Kremlin was named in his honor. Basil walked through Moscow wearing nothing more than a long beard. He threw rocks at wealthy people’s houses and stole from dishonest traders in Red Square.
Few doubted Basil’s holiness. Tsar Ivan the Terrible feared no one but Basil. Basil was also given to eating meat on Good Friday. Once he went to Ivan’s palace in the Kremlin and forced the tsar to eat raw meat during the fast saying, "Why abstain from eating meat when you murder men?" Countless Russians died for much less but Ivan was afraid to let any harm come to the saintly Basil.
I'm not claiming that Pussy Riot is holy in any way, shape, or form. But I wonder if they think of themselves as working in the holy fool tradition. (If so I think they left out a few bits. Celebrity ≠ holiness)