These days, Kulturkampf is usually used in a broad, general sense, denoting a struggle (even a war) between different cultures (liberal vs conservative, city vs rural, religious vs secular, etc.).
Originally, it had a much more narrow and specific meaning. It was coined in mid-1870s by one Rudolf Ludwig Carl Virchow – a highly colorful character (to put it mildly) even by the standards of the Second Reich.
The scope of his interests, occupations, projects and achievements was imply astounding – physician, anthropologist, pathologist, prehistorian (he studied history that took place before written records), biologist, an extremely prolific writer (he published over 2,000 scientific papers – and that was way before the age of word processors), editor, and (of course) politician. He is known as “the father of modern pathology” and as the founder of social medicine, and to his colleagues, the “Pope of medicine” – a no small feat.
He co-founded the political party Deutsche Fortschrittspartei (German Progress Party – no surprise here), and was elected to the Prussian House of Representatives and won a seat in the Reichstag.
His opposition to Otto von Bismarck’s financial policy resulted in an anecdotal “Great Sausage Duel” in 1865 – an event that definitely deserves at least a chapter of some book – if not the whole book.
However, Rudolf Virchow did support the “Iron Chancellor” in the latter’s attempts to (radically) reduce the political and social influence of the Catholic Church, in Germany.
Virchow solemnly stated that the movement initiated by Bismarck was acquiring “the character of a great struggle in the interest of humanity“. During the 1973 discussion in the Reichstag of (in)famous anti-Catholic “Falk Laws” (named after their author, the minister of education Adalbert Falk) he labeled this struggle Kulturkampf.
Hence, originally this term referred to the conflict between the German imperial government and the Roman Catholic Church from about 1872 to 1878, predominantly over the control of educational and ecclesiastical appointments (and more broadly, over secularization policies vigorously pursued by the government of the Second Reich). What made the Kulturkampf unique in Germany compared to struggles between state and Church in other states was its fundamental anti-Polish aspect.
It is well-known fact that Adolf Hitler admired Otto von Bismarck. But it was much more than admiration. Hitler considered his Third Reich to be a direct successor of the Second German Empire established by Bismarck.
Consequently, he fully intended to “finish what Otto von Bismarck had started”, including his war (let’s call a spade a spade) on the Holy Roman Catholic Church over the spiritual and ideological control over Germany.
Hitler was also committed to crushing the Polish Church that he (correctly) viewed as the bulwark of Polish nationalism (and thus of the struggle of the Poles for the independence of their nation).