The church almost executed Galileo for advocating for the Heliocentric model of the solar system. Hard to give them credit for that advance in science.
This isn't really an accurate way of describing it. The Galileo situation is typically misunderstood when people trot it out. There are two things he was in trouble for, one of which (arguably the main thing) was insulting the Pope in his book on two new sciences. He asked for permission to write it, they gave him constraints, and he twisted their constraints on purpose in a way that was basically giving them the finger. I can give you more detail if you like, but the long and short of it was they said it was ok for him to present his new theory so long as he didn't present it as uncontested fact, and showed the current theory alongside it. Instead of doing that he presented the 'alternate viewpoint' as an idiot named Simplicio, who was a stand-in for the Pope, and only said ridiculous things. That's kind of funny, but you have to keep in mind what kind of 'publisher' the Church was at the time (a very cautious one). The other problem was he wanted to trumpet his theory too quickly as fact rather than waiting for others to eventually vet his conclusions. This bears some similarity to the situation for Giordano Bruno, and in terms of the reasons they were in trouble largely having to do with things other than their science (e.g. their behavior, their disobedience, etc).
The main thing to keep in mind is there's a difference between resistance to change and refusal to change. The Church's tendency is and was to be
very slow to accept modifications to its received worldview, and did not want any old crackpot teaching people all kinds of stuff as fact which hadn't yet had a chance to (slowly) make its rounds about the community in a satisfactory manner. This process could potentially take decades or centuries, and this slow-moving change is a bug and a feature depending on how you look at it, but overall is probably more of a feature. It becomes more of a bug when it's slow to change terrible, destructive goings-on in the present tense. It's a very modern conceit to think that a guy has a new scientific model, and they're oppressing him when they don't immediately allow him to begin teaching it as fact. But think of a comparison to, say, a medical guild or association, which doesn't allow new medications or techniques being used until they've gone through testing and been vetted. This is done to protect people, and to protect the reputation of all doctors in the association. Contrast with the proliferation of 'quack doctors' in the early 20th century, where you could not innately trust a doctor to use accredited techniques. So on its face this is reasonable, but what a contemporary person isn't primed to understand is that in the past this vetting process was much slower than such processes are today. But they did have half-way houses for such theory, and it was typically not banned outright. For instance, the Copernican theory was not exactly banned as such, but it was required that it be portrayed as a mathematical model rather than as a physical reality. And good thing too, since it was an inaccurate representation of the solar system.
Galileo and Descartes are the originators of the modern scientific method.
This is the first time I've heard this claim, actually. I've heard it ascribed to Francis Bacon, to various enlightenment people. What did Galileo do that was so revolutionary? I mean, he did invent a tool enabling telescope-based astronomy, improving the field of naked eye astronomy greatly, but there was already astronomy as such. I'm more versed in Descartes' philosophical work than any field work he may have done in science, so I can't be as sure with him, but I don't have any recollection in reading history and philosophy of science books that he's given some special status.
Both came from a Christian society. Descartes claimed to be divinely inspired. But neither was an agent of the church.
I think you're correct in disputing a blithe that anything any scientist said in the past was "the Church" saying it. However it's a complex subject, since you'd have to understand how the vetting process worked for not only doctrine but also issues
related to doctrine but subject to potential changes. It's not really accurate either, though, to say that people who lived under the Church weren't agents of it; that would be to incorrectly separate out their faith life from their work life, which is a fairly recent concept. This is especially so since "the Church" can mean the administrative and ecclesiastical authority in the Church, but also just refers to all the people in it. It's not a monolithic voice, even though the authorities did reserve the right to limit what could be taught as facts.