From what I've read it was mostly the "scientists" of the day - who had been brought up on the Aristotle/Ptolemy model of the solar system - that were yelling for Galileo's scalp. Pope Urban was inclined to give Galileo a pass, but due to the pressure he gave him a wrist slap (house arrest where Galileo could work on his experiments ... which he enjoyed doing anyways). This article makes it sound like it was the Roman Catholic church that initiated this lynch mob -- albeit it cryptically acknowledges some 'nuances'. Rather than describing Galileo's work as "science squelched by organized religion" I believe it more accurate to describe it as an attempt to squelch a new idea, or way of thinking, by entrenched academia.
Your'e correct. The Church in fact gave Galileo several passes. They even send him a letter telling him it's ok to work on his theory, but not to teach it as scientific fact. There were several reasons for this that never attention in modern anti-Catholic society. One was that Galileo's formula was WRONG. Though his theory turned out correct, his formula is still considered defective to this day, just as it was by most of his period peers.
The most notoriously erroneous charge about Galileo today is that the Church was trying to suppress science. It seems nobody can use logic anymore, because Galileo was taught science by Catholic scientists and professors. Galileo got himself into trouble because he became prideful and arrogant, he rebelled against authority and wrote stinging letters of attack against the Pope and cardinals, as well as against learned members of the scientific community. He refused every attempt at mediation.
He never was tortured in any way either, and his greatest 'ordeal' was that he had to stay under house arrest in the Bishop's manse where he studied and wrote until he became old. Some scholars say he was released long before his death. Leave it to the secular media and anti-Catholics to take this case and try to turn it into something it never was.