Is it correct that Gallileo was actually anti intellectual in the sense that his proposals did not follow the accepted methodology?
Him being the equivalent of someone today making claims about some field without doing research(as an example)?
The catholic church not supressing ideas(they had no problem with research) but simply following the accepted norms methodologies and standards of accepting new information as correct.
No, I don't think so. I'm catholic an agree that the popular conception of the Galileo affair is biased, but in favorite empiricism over scholastic theory Gallileo was not acting anti-intellectually. He was very impolite and hasty but challenging the current academic paradigm because you think it could be more rigorous and grounded in observations doesn't make you an anti-intellectual.
But that is only in retrospect since we now think that the modern scientific method is better(and galilleos way of doing things was closer to it).
Imagine these days if someone made claims not based on the methodologies we accept as the scientific method?
Why should the church have accepted his new method? big institutions must be conservative and not jump on any new thing because they risk spending a lot of resources on incorrect rash ideas.
yes. a high-ranking church official even sent him a letter explaining that he was free to continue hypothesising, but he was not allowed to continue claiming that he was right (because he had no real evidence that he was). galileo ignored the letter.
why didn't he have any real evidence? well there's a few reasons. he was claiming that the earth revolved around the sun and basing this claim on observations of the moons of jupiter that he had discovered via telescope.
one problem was that nobody understood how telescopes worked and therefore if what he saw was real. but the big problem was that even if you did believe his discovery was real then it didn't mean that the earth revolved around the sun because moons around jupiter were compatible with the then current model of the solar system (the tychonic model). on the other hand if the earth did move around the sun then all the physics of that time no longer made sense (like, if the earth was moving then why didn't it leave the clouds behind? remember, this is pre-gravity).