While you are correct that Czechia Poland and Slovakia are very similar ethnically and even to some extent culturally, there are some key historical differences that you have to keep in mind.
First of all, Czechia (or as it used to be known: Bohemia) used to be one of the integral members of the Holy Roman Empire, a collection of mostly Germanic states. On the other hand, Poland, before the partitions of the 18th century, had long existed as an independent kingdom or as the Polish-Lithuanian Commonwealth, and modern-day Slovakia used to belong to the kingdom of Hungary. Hungary and Poland had historically been 2 staunchly catholic nations, and that religious ferveur stuck with the people in those regions to this day. Bohemia was the exact opposite. Even before the official Protestant reformation, Bohemia was very fickle in its religious beliefs, as can be seen with the Hussite revolts against Catholic teachings in the 15th century and it’s participation on the Protestant side in the 30 years’ war in the 17th century.
Following the 30 years’ war, Bohemia became forcibly Catholicized under Habsburg rule, casting the Catholic church as an oppressive force in the region. After gaining independence in the wake of WWI, Czechia began to ride on a wave of atheism and anti-clericalism. And after WWII, under the atheist communist regime, this trend towards secularism continued. While Slovakia and Poland also experienced a Communist regime, the firmly planted religious beliefs of the populous remained active after their liberation in 1989. Due to this, Czechia today stands as a bastion of atheism in a region dominated by either catholic or orthodox majority nations.
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Czechia's irreligious current can be seen as a product of the development of it's national identity in 20th century following WW1, as a result of both it's checkered religious history and it's attempt to separate itself from the bonds of Habsburg control after the downfall of the Austrian Empire.
Religious conflict in Bohemia started a century before the Protestant Reformation in the Hussite Movement. The Utraquists solidified their place in Czech culture and identity up until the Thirty Years War and the Battle of White Mountain, after which the Austrians re-catholicized the country. However, Bohemia was never integrated as the Habsburgs had hoped and even though it once again became Catholic, many became part of the church to avoid persecution. Habsburg rule was never without internal trouble and Czech nationalism, culture and language was suppressed. WW1 and the downfall of the Habsburgs provided the opportunity to shed that apparatus, and Catholicism was seen as an arm of that dark period of rule.
In the book Political Catholicism in Europe 1918-45, (alternate link) by Wolfram Kaiser and Helmut Wohnout, the author gives these notes on the topic.
"Prior to the political currents that began the attempt to loosen and release the country from Vienna, especially during the First World War, but also in the period just prior to war, was an anticlerical movement."
From the very beginning, the coalition of people that brought the first Czech president to power, Thomas Masaryk, started to demand withdrawal from the Catholic Church. He declared "We have broken away from Vienna, we will also break away from Rome."
They continue. "The strong anti-Catholic currents in Prague were, on the one hand, upheld by many politicians who had emigrated in the course of the First World War or had withdrawn into inner resistance against the Catholic Habsburg dominance, and on the other, they were upheld by many republican secondary school teachers and by a number of Catholic priests who... contributed decisively to the founding of a 'Hus Church'... By 1921 1.5 million Czechs had already left the Roman Catholic Church. In the early years of the Czech Republic, 150,000 Catholics converted to Protestantism and the 'Hus Church' grew by 500,000 members.... Only in the second half of the 1920's was the proportion of Catholics able to stabilize at around 53 per cent. (From an initial 91%)"
The Hussite Church grew after the first world war, but it's membership collapsed under the soviets.
Additionally, the main apparatus of the Habsburg and Germanic influence in Bohemia was the Jesuits. Ivo Cerman in Jesuit Historiography in Bohemia has this to say on the topic.
"The Czech national movement saw the Jesuits as enemies of the Czech nation, and accused them of a planned destruction of Czech national culture. This interpretation was based on the idea that Hussite conception of Christianity (i.e. Utraquism) was a kind of Czech national religion, and the Jesuit efforts to promote Catholic Christianity was therefore understood as an intentional resistance against Czech cultural traditions...This new national image of the recent past was made popular by the novelist Alois Jirásek (1851–1930), who wrote mainly on the Hussite period. His historical novel, Temno (Darkness), published in 1915, narrated a story concerning the canonization of Saint John of Nepomuk in 1729, and coined a new name for this epoch. The Jesuits were given the role of the main villains in the “Age of Darkness,” which became a label for the whole period of Czech history from the battle on the White Mountain to the beginning of the National Awakening. The term implied that it was an era of a general decline in culture, sciences and national self-awareness, for which the Jesuits were largely responsible."
This national awakening was followed directly by the general Marxist-Leninist policy of atheism. The Current Czech irreligion then can be said to be the product of a long history of religious upheaval. The need to establish a national identity and shed off Catholicism was thus followed immediately by campaigns against all religion by the Soviets, therefore a new 'Hussite' church did not have the time to develop in the new state, furthermore this was followed immediately by the general western trend toward irreligion.
Poland anc Czech Republic (Czechia) is predominantly populated by Western Slavs who speak Western Slavic language and... this is more or less that, when it comes to historical similarities.
After the acceptance of Christian faith by ruler of Poland, Mieszko I in 966 (although the 'Dagome iudex' document suggests that he might have been Christian prior to that date), Poland became a predominantly Catholic country, but in late 14th it entered the personal union with Great Duchy of Lithuania, populated predominantly by Eastern Orthodox population. This close coexistence of two different religions in the two closely intertwined states created the basis for the freedom of faith (equal treatment for all Christian confessions and tolerance towards non-Christans) observed in 16th and 17th century. This was further influenced by generally strained if not hostile relations with Catholic Church due to the conflict with Teutonic Order, backed by the Church, as evidenced by the Council of Constance that started in 1414. This slowly changed in late 17th century in the wake of Counter-Reformation, when the Catholic church slowly regained the dominant status in the Catholic-majority areas.
After the partitions that started in 1772 and culminated in the dissolution of the state in 1795, Polish land were annexed by three neighbours: predominantly protestant Prussia, Catholic Austria and Orthodox Russia. As the treatment of both the Polish populace and the Catholic church in Russia and Prussia was far from preferential to say the least, while the faith was not suppressed as much as a political activity, the Catholic Church slowly grew to be the carrier of the budding popular Polish national identity and culture and thus remained to be an influential institution throughout the partitions and in the revived Poland of the interwar period. Similar mechanism could have also been observed during the post-war era, under Communist rule, when Church, largely opposed by the new government was often collaborating with the anti-communist and democratic underground.
Kingdom of Bohemia shared little similarities with Poland, despite their geographical closeness. Bohemia was considered a part of the Holy Roman Empire since the end of 11th century, and thus the German culture was far more prevalent that it was ever in Poland. This was bolstered by the fact that Prague was an Imperial city and seat of Power in 14th and 15 century. Now, the ill-fated battle of Mohacs in 1526 and the untimely death of Louis II, king of Bohemia, Hungary and Croatia caused the Bohemian crown to be passed to Ferdinand I Habsburg, according to the Jagiellon-Habsburg Vienna Treaty of 1515. This meant that the Bohemia itself became a part of the Habsburg lands with the dynasty strongly supporting Catholic Church. The Habsburg supremacy has been contested from the very start and the defenestration of 1618, when the Imperial emissaries were thrown out the window of the Prague castle is generally considered a starting point of the Thirty Years War. Soon after, when the Czech forces were defeated by Habsburg army in the battle of Bila Hora (White Mountain) in 1620, the victors tightened their grip over the Bohemian lands, forcibly suppressing Protestantism almost to the point of eradcation and pressed further with the Germanization attempts. This situation is generally considered a main cause of modern laity of the Czech populace that, with Catholicism being generally treated as the forcibly imposed religion of the usurper (and being associated with the religion of Habsburg noble officials, it never got much traction among the Czech commoners) and with other religions being basically banned, the ties between Czech culture and any particular religion could not actually form, as already explained by u/Kerlyle.