Nonsense. Again, the Church had the science of the day firmly on its side.
I think CC's point is a bit broader in scope, namely that the Roman Church did not welcome dissent, new ideas and free inquiry.
The Church most definitely did not welcome
religious dissent. On matters of what we call science, however, it did not have any problems with "new ideas and free inquiry". Its guiding principle there was the idea of the "Two Books Doctrine". Revelation via the Bible and the Church Fathers ("the Book of God") was held to
always be fundamentally in harmony with rational inquiry into the natural world and natural philosophy ("the Book of Nature"). So in any cases where one
seemed to be in conflict with the other, they thought the issue always had to be one of interpretation. This meant either the understanding of the scriptures or Patristic writers was wrong and needed to be reinterpreted, or the understanding of the natural world was in error and needed to be better understood. This is why when early Christian thinkers came to reconcile Greek natural philosophy with their faith and there seemed to be a clash between the rational evidence that the earth was round and various Biblical passages that talked about it being flat, it was the latter that got reinterpreted, not the former that was rejected.
It's also why when Galileo's telescopic observations and the implications of the comets and the supernovas of 1573 and 1604 pretty much dealt a death blow to some fundamental principles of Aristotle's cosmology, it was the Jesuit astronomers of the Collegium Romanum who confirmed these developments, lauded Galileo's discoveries and honoured him with a degree, medal and banquets, along with audiences with the pope and various leading cardinals, while Galileo's conservative academic peers still clung to Aristotle. It's also why when Cardinal Bellarmine - the learned natural philosopher and theologian who later presided over the 1616 Inquisition into Galileo's forays into theology - observed the state of the cosmological issue of heliocentrism in 1615, he said "if there were a true demonstration that the sun is at the centre of the world and .... the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary, and say rather that we do not understand them than what is demonstrated is false". In a period before scientific revolutions and discoveries became commonplace, all intellectual institutions were highly conservative. In that context, the Catholic Church of the early 1600s was actually much more open and nimble than most.
Free inquiry, new ideas and dissent on matters of religion, however, were another matter entirely. Prior to 1616, no-one in the Church cared about Galileo's heliocentrism. His discoveries and other ideas were, as I've noted, acknowledged and celebrated. His adherence to a highly marginal conception of Copernicus' model as being actually
true was known and considered eccentric by both clergy and fellow astronomers, but it didn't bother anyone in the Church. In 1613 Galileo published his
Letters on Sunspots (
Istoria e Dimostrazioni intorno alle Macchie Solari) which not only made his Copernicanism absolutely clear but also used several arguments in its favour that he later used in his
Dialogue Concerning the Two Chief World Systems (1632). All legal publications had to pass censorship scrutiny in this period and in this case the Letters were scrutinised by the Roman Inquisition before publication. Apart from some quibbles over his use of some scriptural references, the book was passed for publication. Its heliocentrism didn't bother anyone. What changed in the intervening three years was Galileo making increasingly public and increasingly vocal pronouncements on Biblical interpretation in relation to his ideas.
That was what got the attention of the Inquisition, because in the tense political and theological environment of the Thirty Years War and the Counter Reformation, a "mere mathematicus" taking it upon himself to interpret the Bible was a no go. Galileo managed to entangle his science with theology at exactly the point where the Papacy was under pressure to be more vigilant about things like laymen deciding they could interpret scripture. If he hadn't done that, it is very likely he would have been left to his strangely marginal ideas, much as Kepler and many others at the time were.
Had it's behavior been so I think it fair and accurate to conclude that it would have had science on it's side. And I don't think I'm guilty of anachronising here.
Its "behaviour" is beside the point. The simple fact is that in 1616 when the whole Galileo Affair kicked off, the overwhelming consensus of astronomers was that Copernicanism simply did not work as a physical model of the cosmos for a range of purely scientific reasons. As a result, in the period between 1514 and 1616 we can find
just 13 writers of any kind, most of whom were not astronomers, who accepted Copernicanism as a physical system. Galileo was championing a fringe theory held by almost no-one, while the Church was working from the massive consensus of the current thinkers in astronomy of the day.
The Church had science on its side. This is why the 1632 ruling against Galileo famously says his ideas are "foolish and absurd in philosophy;
and formally heretical". "Philosophy" here means "natural philosophy", specifically astronomy. They found him to be
scientifically wrong and, as a consequence of that, in contravention of standard interpretations of scripture.
All that aside, Cheerful Charlie went far further than claiming the Church "did not welcome dissent, new ideas and free inquiry". He clearly made a series of historically erroneous statements like "The RCC was not doing careful science here, it was doing ancient and wrong dogma". That's garbage. The Inquisitors were not scientifically illiterate idiots - they were among the most learned men of the day and Bellarmine had taught natural philosophy at the University of Leuven before coming back to Rome. They were well aware of the consensus of astronomers and received a scientific assessment of Galileo's arguments for Copernicanism in light of that context, which laid in detail why almost all astronomers thought he was scientifically wrong. Cheerful Charlie completely misrepresents that scientific context and clearly does not have a detailed grasp of the relevant historical facts. It's never smart to make loud pronouncements about history if all you're doing is working from some popular conceptions and bit of Googling.