It has nothing to do with what each supports - rather that you can't justify harmful behaviour, period.
> Russian Orthodox church going out of its way politically supporting Putin (and immensely benefiting from that financially and politically) isn't a doing of Jesus work, and challenging the church on that isn't an assault on Christianity.
Challenging the church regarding their supposed support of Putin isn't the problem, using it as a justification for illegal behaviour is. What Pussy Riot did would be illegal in pretty much every reasonably civilized country in the world.
In Canada, people spray painting political graffiti on a synagogue is a crime, even if the content of the graffiti isn't necessarily insulting to Judaism. The point is that you can't arbitrarily allow some types of crime, and disallow others based on the ideology behind it...