The narrative of Galileo vs the Church is misrepresented to push a specific narrative, the whole thing is obviously very nuanced, but to keep it short he was in disagreement with the Church, but he was a Catholic himself who happened to live in a period where the Church was on edge due to the tension with Protestantism. The fight wasn't on science vs religion, but on who had the religious authority, individuals or the Church.

Galileo is portrayed as a proto-skeptic later on because it was useful to present the European enlightenment as a rupture with the old world, nevermind that Europeans pushed racism as a science while claiming to be purely rational, you can see this kind of misrepresentation of many early scientists as well such as Newton, who's obsession with esoterism is rarely discussed, and even when promoting a grand narrative of the West as the cradle of reason people like to ignore that as far as we know Pythagoras was a weird religious dude with a cult, you don't need to be rational in all spheres to be rational in some, and if we want to highlight the diversity of western thought as a good thing (which I believe it is) we can also find examples of early skeptics way before the enlightenment. Cicero literally wrote a skeptic as one of his characters to express his ideas, and while he's clearly trying to promote stoicism instead, the fact that he includes a skeptic shows that there were already skeptics in society even back in Rome. And again, in my opinion this is a good thing, we generally need more skepticism, not less, but let's not reinforce narratives that are just false and used to whitewash the horrendous crimes of colonialism to this day.