That too. Several objections to Galileo's model were based on real observations, which means science. There were sound scientific reasons to reject his model despite the fact that the core of it was a vast improvement. It's an interesting scientific contradiction.
Then they should have just published their own objections. This in no way justifies the persecution of Galileo, which was basically akin to the Soviet persecution of Sakharov -- like him he was under house arrest and forbidden to interact with the scientific community at large.
In a way the same is true for Galileo: he was only really prosecuted after writing a book in which he called the pope (who was up til that point friendly and open to his views) a fool.
Bad lesson from this (completely valid) analogy: by 1970s, Communism has become a full-blown religion, with it's pseudo-scientific roots being thoroughly debunked, but politicians resting on them stubbornly refusing to give way.
That's not even a bad lesson: it is possible to interpret Communism as a radical Christian sect, which, having done away with God altogether, tries to build Heaven on earth. This way, its core beliefs do make sense...or rather, they're internally consistent.
(And I wish you'd stop this nonsense of implying that Galileo had his own special heliocentric model. He didn't; he was advocating the model of Copernicus.)