I support the idea that people are people and not property and have rights, which is something that ATL has repeatedly rejected, as does Abrahamic doctrine.
Trial by jury, in some form long predates the Papal Inquisition.
Yes at times members of the clergy have played a role in science and the expansion of knowledge. In part because their often have the time and resources to spend time on such projects. One of the great early steps in the revolution that lead to modern science was Occam's Razor. In some versions it is stated however that he adds a rider that this doesn't apply in matter of church doctrine which suggests that he was restricted on that issue.
Did the church, Catholic or otherwise, promote the Scientific Method or were they so dominant in science because they sought to monoployise knowledge?
You mean that Galileo whether he was totally accurate on the fine details or not had to recant on the idea that the Earth orbited the sun because a bunch of thugs threatened to murder him rather than have their decisions questioned?
You only have to look at the arguments put forward by ATP to see the virtual identity with the doctrine of both the Nazis and the Communists. The party is always right and should never be questioned and any opposition must be ruthlessly crushed.
Note - I'm not saying there are no good Christians, Jews or Muslims. There are many, many millions. However that's largely because their humanity and morals override the constraints of 'their' religion.
OK, you had to go to Galileo. I knew you would. But first to address your other points.
Catholic Doctrine has never viewed people as property, as evidenced by the enormous volumes of material of the Church condemning the slave trade. Catholic doctrine is also the first place we see in the world the concept that a true marriage requires the consent of both the husband and wife, free of external coercion.
And yes, 'in some form', but the Papal Inquisition codified the forms that we use to this day as well as greatly expanding the rights of the accused far beyond anything seen in any of the earliest forms of 'jury'. Indeed, the entire concept of requiring the accuser to prove their accusation true rather than the accused prove the accusation false is an innovation that came directly from the Inquisition.
The Catholic Church has always promoted science, full stop. It is Catholic Doctrine that God intended for us to understand His creation, which is why he gifted us with Reason and the desire to do precisely that.
Now to our good friend Galileo.
The very first thing to understand is that Galileo was an utter and complete asshole, a total jackass, a plagiarist, a vulgarian, and all in all an incredibly unpleasant human being. None of his contemporaries even liked him, few respected him. If you asked any other scientist of the day, including those who agreed with him, their opinion of Galileo it would be unprintable, and if it had been up to his fellow scientists he'd have been drawn and quartered on general principle.
But the Pope thought he was a genius, so Galileo was protected. Indeed, the Pope was Galileo's patron, financed all of his studies, paid for all of his expenses, and provided his housing and work spaces. This was a major part of the reason why Galileo was such an arrogant ass to everybody else.
Then Galileo got a bit too big for his britches and in the course of a heated exchange of letters started making theological proclamations on doctrine. He was not trained in theology, and his proclamations were, to be blunt, ignorant as hell and focused purely on advancing his own personal claims.
The Papal Inquisition called a foul. But contrary to popular belief, this involved him being summoned to Rome, where he stayed in the Papal apartments as an honored guest of the Pope, and the Inquisition's notes and transcript of the hearing about his conduct survive. Cardinal Bellamy walked on eggshells around him, and in the end the Inquisition pretty much lightly tapped him on each wrist with a pool noodle and told him to stick to science and leave theology and doctrine to the Church, which Galileo agreed to do.
While he was in Rome, the Pope commissioned a new book from Galileo. The Pope had been following the arguments among astronomers over Copernican theory and requested that Galileo write a summation of the arguments for and against, with recommendations on what avenues to pursue to resolve the argument one way or the other. The Pope's commission explicitly desired a defense of Copernicus.
As a digression. The Copernican model of planetary movement had one major flaw, all orbits were perfect circles, therefore the model failed at predicting the movements of planets beyond a few days and could not account for retrogression and such. The older Ptolemaic model, while completely wrong physically, was exceptionally accurate, so much so that it was still in use for precise orbital position calculations into the 20th century.
Galileo accepted the commission, took the money, and wrote the requested book.. only he didn't write the book the Pope wanted him to write. Instead he wrote a book in a somewhat older style of writing in which the Wise Teacher (Galileo) is explaining to the Idiot Student (Simplicus, who was a blatant expy of the Pope himself) why the Idiot Student is an Idiot and the Wise Teacher is condescending to explain why in terms even a total dunce could understand.
With this Galileo made his final mistep. He'd directly insulted, personally, his patron, and his swarm of enemies pounced. He'd by this point pissed off *everybody*. But even then, when he got hauled back to Rome, he wasn't tossed into durance vile or mistreated, he simply was put up in a less grand apartment than before, and was pretty much given a much firmer slap on the wrist than before. The main punishment was he was banned from correspondence and further writing, because bluntly nobody wanted to deal with his shit anymore and the Pope was unwilling to continue to protect him from literally every other scientist in Europe.
But he still lived out his days in the same comfortable quarters provided by the Pope, with his expenses still paid for by the Pope.