I am someone who read all the research that agreed Galileo was arrested and threatened by the Church. One English professor dissents.
The Galileo affair was complex, and has frequently been boiled down to simplistic and polemic science-vs.-religion sound bites.
First, Galileo was primarily a physicist, not an astronomer. His work in physics continued unmolested by any religious authority.
The church's own scientific authorities (the Jesuits) took a look at Galileo's work and agreed with his celestial observations. They simply maintained that his interpretations of those observations were not necessarily proof. They were open to accepting revised views of the natural world if convincing proof were found.
The fact is, Galileo had an interpretation, but he did not have proof of the motion of the earth. It was difficult for people prior to the 17th century and Newton's first law of mechanics, to understand how a rapidly rotating planet earth could even be plausible.
On balance, the Catholic church was always open to amending views of the natural world based on the current state of knowlege. That philosophical posture goes all the way back to Saint Augustine.
The context for how things went south for Galileo is largely political, not religious.
First, Galileo was an arrogant and offensive person who made many powerful enemies.
Second, Galileo's assertions were made in the context of the Catholic counter-reformation at a time of intense Protestant-Catholic conflict. At that time, the Catholic church was hunkered down in defensive posture, and were keen to repress the Protestant mantra of individuality and repress the Protestant revolt against authority and receieved authoritative wisdom.
