All the nations of the Warsaw Pact aren't actually extremely religious, with East Germany being the best example. The German states which compromised the German Democratic Republic have an officially declared atheism rate of about 90%+, which shows the success of the former communist establishment in eliminating religion.

For many other nations it's a case-by-case basis, in Russia the state has heavily supported the Russian Orthodox Church since 1990, turning it into something of a state religion. Putin and the ROC have entered into a mutually beneficial relationship, where the ROC leaders benefit, and in turn support Putin politically.

In many other cases the religious establishment would often have ties to the communist governments, although they'd also symbolize resistance (like the Catholic church in Poland). While the governments would sometimes try and stamp out religion, they often didn't try that hard.

In the case of Poland, there has been a thousand years of tradition of Catholicism as an integral part of the idea of a Polish nation. Whilst the state was more confessionally mixed until the ethnic cleansings of first the Germans (Jews, Gypsies etc.), then the Soviets and their 'Little Stalin' puppet communist regime, (German, Czech, Russian, Ukrainian ethnic Poles). These two unpleasant events combined to make Poland from 1945 the most ethnically homogeneous nation in Europe. The Polish-ethnic Poles had a rate of Catholic religious observance slightly above 90%, and now almost all the citizens of the nation were Polish-ethnic.

The efforts to disrupt the Church occured mainly between 1949-1956, at which point there was an stalemate between the Government and Church, with the Church slowly gaining the upper hand though the 1970s, and from 1978 with John-Paul II becoming the Pope, religious observance, as well as the Solidarity Union, became the two focal points of resistance, (in 1976 the pilgrimage procession of the Black Madonna attracted half a million visitors, despite the government building a motorway across the route to prevent easy access) and between them played a very important role in the transition to a democratic regime.

In the economic reforms overseeing the dismantling of the command economy in the Early 1990s, the Church continued to provide an important role in emphasising the role of civil society, limiting some of the excesses that occurred in other states such as Russia, though many people were less keen on its attempts to outlaw and de-liberalise the abortion laws in Poland.

Thus in the case of Poland, the Church (and so religion) has an important and traditional role, not only in national identity, but in recent history and the maintenance of civil society against both Communism and the problems created by neo-liberal economic policies.

This map surprises me, and I'm kind of curious about it too. It should be noted, though, that Western Europe is probably more the outlier than Eastern Europe, as can be seen on this map and some of these maps.