That was the greatest assault of the Devil on Christ's church since Nero. Mother Russia has never recovered. The hostility to this saintly Pope is another symptom of the wounds that still bleed.
A docile remnant survived physically and is now known as the Orthodox Church in Russia. Initially, few churches were allowed to operate; in rural areas a visit to church could take days. The buildings of the closed churches were desecrated and blown up. Being of solid construction, the stone carcasses still stood. Crows nested in the broken cupolas. The icons were typically rescued by the peasants and hidden in homes. Public religion became the domain of fearless grandmothers and intimidate beyond their wits know-nothing priests that learned to colaborate with the state.
Stalin's near demise in The Second World War in 1941 produced an accomodation. A few more churches were allowed to reopen and persecution of the state-recognized church officials stopped. In return the Church anathemized the Germans and blessed Stalin's regime.
Honest, even heroic priests continued to do their duty in slowly reaching out to the younger generations and teaching the universal values. Nevertheless the Seminaries were wholly penetrated by the agents of the state and the average priest would studiously avoid any political controversy.
There is no reason to think that the interpenetration between the state and the church is any less today. Indeed, it is compatible with the Orthodox model of church-state relations, and the modern Russian state seems to be genuinely sympathetic to the church. Putin, for example, seems to be a church going Christian and so was Yeltsin.
It is entirely possible that the secular forces of the Russian state had an informal say in the Patriarchy's rejection of Vatican's entreaties, but of course, some people need to die or at least retire before we know, -- if ever.