Very similar question (also including Slovakia) has been asked recently, so until new responses come in, you might be interested in this thread where the issue has been addressed.

There are some good posts here, but I do want to add a bit of a caveat to the claim in the original question that Czechs are among the most atheist countries. They might not attend church regularly, but they still very much view themselves as a culturally Christian country.

Czech identity was recreated in the 19th century during a period of time known as the Czech National Revival - the essayist Vladimír Macura famously said that "Czechs live in a very long 19th century" (a play on the idea that the period between the French Revolution and WWI is a long 19th century) - and Czech identity today still rests on much of the religiously-couched liberalism of that time. Between the early 17th and 19th century, the Lands of the Bohemian Crown (which today are roughly the modern Czech Republic) were an integral part of the Habsburg monarchy. During this time, Czech was still spoken by roughly 2/3 of the population, but German replaced Czech as the language of politics, commerce, culture, and academia. In the 19th century, a small group of linguists and historians began to try and reconstruct an independent Czech language and cultural world which would be equal to the German cultural world. During the National Revival, historical events from the medieval Kingdom of Bohemia were 'revived' by a small group of urban intellectuals who simultaneously rewrote Czech history and rebuilt (and sometimes entirely fabricated - Macura focuses on this quite a bit in "Mystification and the Nation") the Czech language which had been in steady decline in high society since the Battle of White Mountain. The recreation of this nation was largely in an effort to justify their nation building project, and it tried to present Czech-ness as an equal Other to German-ness. In his fantastic book The Coasts of Bohemia, Derek Sayer says that "this modern nation is not so much rooted in that medieval experience [of the Kingdom of Bohemia] as retrospectively reconstructed out of it."

One of the most important historical periods that Czechs invoke in their symbolism and nation-building projects is the Hussite period. People like the 19th century historian Franišek Palacký and the First Czechoslovak President Tomáš Masaryk saw the Hussite movement as an expression of Czech culture first, as a religious uprising second. Masaryk in particular saw Czech history as an evolving system of values he vaguely dubbed ‘humanism’, and he believed that this belief-based definition of the nation peaked during the Hussite period. By divorcing the Hussites from historical context and turning them into a symbol which could be evoked as representative of the Czech nation, Czech nation building allowed for easy re-purposing of historical events for contemporary political projects. This is why the Hussites were also so important for the communists. The radically communal peasant elements of the Hussite movement known as Táborites were easily turned into class warriors because they were symbols of Czech identity. While he is careful to avoid claiming that communism was an inevitable result of 19th century romantic nationalism, Derek Sayer argues that “Hus, Žižka, and the Táborites could be recycled as class warriors because … they had been thoroughly contemporized and secularized as heroes of this ‘popular’ nation” by the Czech Revivalists and Realists over the previous century.

You can see this direct line between the Kingdom of Bohemia and the modern state in the Czech Republic's 1993 Constitution. The preamble begins with "We, the citizens of the Czech Republic in Bohemia, in Moravia, and in Silesia - At the time of the restoration of an independent Czech state - Faithful to all good traditions of the long-existing statehood of the lands of the Czech Crown, as well as of Czechoslovak statehood..." It clearly states that the modern state is a restoration of the traditions of the medieval state. The fact that Czechoslovakia’s failure to create a functioning multinational state is a significant reason for the Velvet Divorce is lost in this preamble. Instead, the Czech Republic signifies the national myth by connecting the new state with the medieval memory. Later on in the preamble, the Czech people are said to be "resolved to guard and develop together the natural and cultural, material and spiritual wealth handed down to us." The resolve to develop, among other things, cultural and spiritual wealth “handed down to us” outlined in the 1993 Constitution is no different from how Masaryk or Nejedlý used historical symbols to mythologize a natural, driving project to define the Czech nation.

While Czechs may be the outlier in degrees of expressed religious belief among postsocialist countries, there is still a great deal of cultural Christianity within Czechness. I won't explore the implications that this facet of Czech identity has when it comes to non-Christian migration into Europe, but it does offer an explanation of why a country where under 30% of the population believes in God would vote to make Good Friday a national holiday. A great place for people who are curious about attempts to reconstruct identity in postsocialist countries to start is Svetlana Boym's The Future of Nostalgia and in particular what she calls Restorative nostalgia, which she claims to be at the core of 21st century national and religious revivals.

Bibliography of works not linked:

Boym, Svetlana. The Future of Nostalgia. New York: Basic Books, 2001.

CZ Const pmbl., 1993.

Masaryk, Tomáš, The Czech Question, trans. Peter Kussi, 1895

Sayer, Derek. The Coasts of Bohemia, 1998.

Macura, Vladimír, The Mystifications of a Nation: The “Potato Bug” and Other Essays on Czech Culture, ed. Hana Píchová and Craig Cravens, 2010.

Part 1/2

This is a very complex question, which contains some assumptions as well. I might not be the best to answer on the complicated topic that is the history of Poland, which is a country that doesn't even share much of it's geographical position with the Poland of 100 years ago, but I will present some data on the Czech Republic.

Czech Republic is a country of about 10million people, it is also known as the historical area "Lands of the Czech Crown", Bohemia, Moravia and southern Silesia (the borderland with Poland).

It was Christianized from 2 directions. Bohemian nobility was baptized in January of 845 in Regensburg, as we know from Annales Fuldenses, but Moravia had for some limited amount of time ties to Constantinople as well through the mission of Saints Cyril and Methodius in the 860s. Later, their influence expanded to Bohemia as well and for some time, two competing churches existed in the Czech lands, although Bohemia became almost fully Roman Catholic in the span of several decades, with the work being attributed to Saint Wenceslas, while the first Czech laws, Bretislavova dekreta (http://www.psp.cz/eknih/snemy/b_dekreta.htm) clearly deal with existing pagan practices more than 100 years after the death of Saint Wenceslas. The issue was eventually solved by later lords, who pushed away all pagans and followers of non-Roman Catholic Christianity.

In the century following Bohemia becoming an ally of Rome, it became a place from which Catholics organized their missions to Prussia, Poland and Hungary. The most famous one being the Mission of Vojtech (Adalbert).

However the memory of conflicting concepts of Christianity existed in the Czech traditions, even though many followers of Cyril and Methodius converted to Catholicism quite soon. In the late 14th and early 15th centuries, a movement under Jan Hus started in Prague. It's goal was to reform the catholic church. https://www.britannica.com/biography/Jan-Hus When Hus, a very popular preacher and former rector of the University of Prague was called a heretic and burned at the stake at the council of Constance, a religious war started in Czech lands, creating a new wave of Christianity called the "Hussite movement". It proved extremely powerful, defeating 5 crusades in row and eventually turning into a moderate protestant church, the Unity of the Brethren, that existed and held a lot of power in politics until the 30 years war. During the war, it was banned and Catholicism was forced on Czech lands by the Habsburg dynasty. The seat of the Holy Roman Emperor was once and for all moved from Prague and The Habsburg and later Habsburg-Lorraine rulers held firm ties with the Roman Catholic church. Until 1781 it was the only legal denomination and even long after that not all protestant churches were allowed to function, the Unity of the Brethren was legalized as late as 1861.

However, since the Czech National Revival already existed for some time, many people, especially nationalists, started associating the church with government oppression and from a modern secular point of view it is understandable. For example the book "Mala kniha ke cteni pro zaky Obecnych skol, Uceni nabozenstvi", Prague, 1853, which was by the order of the department of education number 2875 from 21st April 1850 the only legal textbook to be used in public schools to teach this subject, contains explanations to the 10 commandments, one tells students that the 4th commandment also means that all people must obey their nobility and government officials, no matter the circumstances. (pages 54-56).

As the Czech nationalists failed in various attempts of gaining political power, most importantly the revolution of 1848 and later in gaining independence not unlike the Hungarian part of the empire, more and more Czechs and Moravians supported nationalist movements, freethinkers and republicans. During WWI, many of those forced to serve in the Austrian army deflected to France and Russia, creating so-called "legions". These legions became quite known, one even fought the bolshevik revolution and for some time took control over Siberia and because of them, the Newly created Republic was considered as a force that fought against the Central Powers. The Republic also gained Slovakia, a land in the North of Hungary and a small part of territory called Carpathian Ruthenia.

Slovakia and Carpathian Ruthenia were regions with many strong believers, Moravia, especially the countryside was somehow catholic with protestants as well, but Bohemia was very strongly dissatisfied with Catholicism. During the period known as the First Republic, between the wars, Czechoslovakia was in a a conflict with Vatican and nuncio Francesco Marmaggi was even recalled from Prague.

The political representation of the believers was the Czechoslovak People's party (CSL) and had 7-12% support between the wars, although there were pro-catholic forces in the Agrarian party as well.

After WWII, CSL was one of the few parties allowed to participate in the elections and was the only non-socialist party in the Czech lands. It gained around 20% votes in 1946, as many Agrarians were voting for CSL when Agrarian party was not allowed to participate any more. During this time the demography of the Czech lands changed as it lost it's Jewish and German populations. Czechoslovakia itself also lost Carpathian Ruthenia.

Please note that the "89%" is the number of people in Poland who were baptised. This includes people who are not religious in any way, which includes yours truly. The actual religiosity in Poland is much lower and in unevenly spread between generations. Among people below 40 it's on the level of an average European country and among the youngest adults (below 25), the religiosity is actually lower than the European average. It's the oldest generations who are highly religious.