In the case of the German and Polish Catholic Churches, they're even under direct control of the Vatican, i.e. the Catholic Church proper.
Yes, your local community may be good and if it's an independent church like most religious groups in the US are, it may be completely removed from any greater politics but Catholic churches are very much part of the Catholic Church proper (i.e. if a priest steps out of line, they risk being removed -- which btw is exactly what happened when a Catholic priest in Germany in the 1990s openly preached views that the Church considered too progressive).
A small religious community may hold okay views and be nice and dandy, but organised religion (and especially the Catholic Church) is rotten to the core. And I say that as a baptised & confirmed Catholic in Germany.
This is incorrect. Its original meaning is "assembly", "meeting" and refers to a group of people more than a building/denomination/organization: https://www.compellingtruth.org/definition-church.html.
The conversation was clearly about organised religion, i.e. specifically the Catholic Church (in Poland or Germany but also in general as a larger entity). It doesn't get much more organised than the Catholic Church.
It was also clear that "church" in this context is used in the sense of "a formal religious organisation", especially because churches as formal organisations are legal entities in these countries.
What the term _originally meant_ is interesting but utterly irrelevant given that the meaning clearly doesn't match the intended meaning and the intended meaning is widely enough understood (and matches the Polish and German equivalent terminology).
That said, linking to a website operated by a conservative Evangelical ministry that preaches Young Earth Creationism and considers Catholic "non-Christians" ... in a conversation that's primarily about the Catholic church ... is "funny" to say the least.