The Church of Christ the Saviour is the perfect symbol of what is wrong about modern Russia. In 1931, Stalin dynamited the place to build a monument to Communism. In the 1990s, as the Soviet Union was no more, and the Orthodox Church assumed new powers and reassumed its role as apologist for the state, Boris Yeltsin decided to rebuild the church. Hundreds of millions of roubles later, a garish gold and marble structure was unveiled. It has become a monument to the mix of power, brute force and bling that is the hallmark of the rule of Yeltsin's successor, Vladimir Putin.

The church is now at the heart of the struggle for freedom of expression in Russia. In March, the three members of the punk band, Pussy Riot, sneaked in to perform a guerrilla gig, denouncing the former KGB chief for muscling his way back to the top job of President. Their song – "Virgin Mary, Chase Putin Out" – lasted about half a minute. Nadezhda Tolokonnikova, Yekaterina Samutsevich and Maria Alyokhina were thrown in jail, charged with "hooliganism" and inciting "religious hatred".

The show trial that has taken place since the end of July is widely regarded as a PR disaster not just for the church but for the Kremlin.

These two immobile and all-powerful organs of power have, so we are led to be believed, been humiliated by three sassy young women standing in a courtroom cage dubbed "the aquarium" and using their court appearances to deliver punchy and dignified denunciations of the authoritarian regime.

This narrative, which puts a contemporary context on to the travails of the likes of Aleksandr Solzhenitsyn and Andrei Sakharov, is half right and half wrong. On Friday, the three will be sentenced. The verdict is in little doubt. The only question is the length of sentence, with predictions that, on Putin's instruction, they may receive less than the three years maximum.

The women's cause has been taken up by artists from Yoko Ono to the Red Hot Chili Peppers and Franz Ferdinand. Madonna used a concert in Moscow to rally to their defence, scrawling "Pussy Riot" across her back and performing "Like a Virgin" wearing the band's trademark balaclava. As if on cue, Russian deputy prime minister, Dmitry Rogozin, played perfectly to her audience by denouncing Madonna on Twitter as a "slut". He added: "Either take off the cross or put on pants." A "world rally" has been promised in the event of conviction.

This was a fight Putin did not need to pick. With a word in the ear of the prosecutor's office, the Kremlin could have defused the problem. The Riot's original protest gained some coverage, but not as much as others in the past such as Voina, the radical art collective, of which they were members.

Voina's first action was to stage an "orgy" in 2008 after Dmitry Medvedev became president – claiming that sex in public was no more obscene than rigging an election.

Only the most myopic authoritarian would regard protests such as this a threat to the system. Since "persuading" Medvedev to swap jobs and return to the job of Prime Minister earlier this year, Putin has allowed his thuggish personality to get the better of him. He has arrested a popular opposition leader, Alexei Navalny; denounced a popular female TV presenter and "socialite", Ksenia Sobchak, and targeted a former deputy prime minister Boris Nemtsov. Meanwhile, the rubber-stamp that passes for parliament has passed laws punishing public protest and requiring non-governmental organisations to register as "foreign agents".

One might therefore think that Putin and his cronies are about to collapse under the weight of their own contradictions. That is the message his opponents like to tell. This is wishful thinking. Not only does Putin exert absolute power over political and security structures, but he has yet to create the anger and the hunger for change that led to the Arab Spring.

For sure, many members of the Moscow and St Petersburg middle class are embarrassed by what they see. These well-travelled folk regard Putin as uncouth. Medvedev was more their man, a leader who was polite to foreign dignitaries and whose language is not peppered with vulgarities. He promised a "law-based" society and a clampdown on corruption. Neither bore fruit; then last autumn Medvedev acceded to the still mysterious job-swap with his real master.

So now Russians are lumbered with Putin – not that he had ever left the scene anyway. During his first two stints at the top, he was relatively adept at managing the message. With the aid of PR advisers, the Kremlin took to social media and television to proffer the line that Putin provide the only guarantee for social stability and wealth creation.

For the moment, that line remains convincing for most, at least until a credible alternative arrives. No matter how articulate and telegenic three female punks might be, they are not about to send the system crashing down.