It's odd how far people have run with simplified versions of Galileo's story. The version I've seen everywhere is "The dastardly anti-science Church hated heliocentrism so much that it persecuted Galileo for it." The Church's support of geocentrism did play a role, but if you look at the details, it seems far closer to "The Roman Church of Galileo's day was filled with scheming politicians, and he (perhaps unwittingly) offended people who he couldn't afford to, so his enemies latched onto his support for heliocentrism as an excuse to get rid of him."

These days, I've come to treat every clean-cut historical anecdote as suspect; there's too much of a game of telephone between people who want history to prove their point.