Ptolemy was revered for his (incorrect) wisdom. Copernicus had to keep his (correct) wisdom in the closet for religious reasons and it wasn't until Galileo dared to insult "society" by suggesting that we can progress wisom with knowledge that he was shunned from society for religious reasons
That's a nice slant.
Copernican heliocentrism as touted by Galileo was inaccurate, as were many of his supporting theories around tidal movements etc. It assumed that planetary bodies traveled in a circular rather than elliptical orbit and that tides were caused by the sloshing of the seas as the earth sped up and slowed down in orbit. When the science was questioned over the fact that there was no noticeable stellar parallax that could be determined with equipment at the time (hotly discussed even in the 21st century), Galileo turned to personal attacks on individuals which landed him in hot water with the Catholic Church.
The idea that the church at the time was ignorant of science or thought that the world was flat is simply not true.
Any link between Galileo and a minority group making demands over a democratic majority to force cultural change is tenuous at best.