It is common knowledge that in 1633 that Galileo was tried for heresy by the Church. Also well known is the subject area — he had just published Dialogue Concerning the Two Chief World Systems, espousing a Copernican view of Earth's motion, contrary to contemporary interpretation of scripture.
15 years prior, Cardinal Bellarmine had declared Copernican heliocentrism to be false and contrary to scripture, but allowed for its discussion as a hypothetical model for understanding scientific observations. So Galileo eventually ran afoul of the Church not for putting forward a heliocentric model, but for failing to frame it as a purely abstract model.
If you live near Kansas, this likely sounds familiar.
Galileo also made a political error in accommodating Pope Urban VIII's arguments by use of Simplicio, the straw-man advocate for Ptolemaic geocentrism in Dialogue. But Simplicio was not a stand-in for Church authority, for the character was already present in the text and represents many Aristotelian perspectives beyond geocentrism.
It is from the original inspiration for Simplicio we can draw a modern lesson. "The pigeon" Lodovico delle Colombe was a staunch defender of existing models of nature, including not only an immobile Earth, but also a perfectly spherical moon (all heavenly bodies must be pure) and buoyancy based on form. Galileo was a figure of controversy because he dared to question the way people were raised to understand the world, presenting alternative views that align with observed measurements.
When Pope John Paul II famously apologized to Galileo in 1992, he summed up this faux pax:
[Galileo] rejected the suggestion made to him to present the Copernican system as a hypothesis, inasmuch as it had not been confirmed by irrefutable proof.
Centuries later, a large population considers only the teachings of our parents irrefutable, and insists that evolutionary speciation, anthropogenic climate change, or collectivist economies must be carefully disclaimed as abstract hypotheses. It is important not to let these pigeons dictate the role of science in our culture.