[Keysh]

the church rejected it because it did not fit observations (the ultimate scientific reason).

No, the Church rejected heliocentrism because it clashed with scripture, and because Giordano Bruno had promoted it, so they associated it with heresy. Their argument was that it was OK to use heliocentric models purely as calculational devices, as long as one did not attempt to argue that it somehow reflected reality. The Church did not begin to formally accept heliocentrism until the 1750s, when they dropped the general prohibition against heliocentric books. The prohibition against Copernicus's book De Revolutionibus was only rescinded in 1835.

[mcv]

That the church rejected heliocentrism because it clashed with scripture is a common misinterpretation. It had nothing to do with scripture, and indeed scripture says nothing definitive about it in a way that would trump observation. The church did not have a problem with heliocentrism before Galileo started picking fights over it, and it seriously considered Galileo's model. Galileo's model did not match the observations of the time though, because Galileo insisted on circular orbits, which was wrong. (Who knows what would have happened if his model had been shown to match observations?) When Kepler proposed a model with elliptical orbits, Galileo even ridiculed that idea.

Once Galileo had fallen out of favour with the pope for insulting him (in a book that was supposed to be an evenhanded comparison of geocentrism and heliocentrism, he had a character called "Simplicio" repeat arguments that the pope had used), he got investigated for that, and eventually got house arrest. It's entirely possible a heresy charge got piled on top at some point, but that's not how it started; the pope was entirely willing to consider heliocentrism. And Galileo was not the first to propose it either.

Perhaps it should be mentioned that Kepler actually had religious reasons for proposing his heliocentric model, believing the sun to represent Jesus, around which the universe revolves. That didn't stop him from using observation, and thus science, to perfect his model.

Many of these people held what we now would consider pseudoscientific beliefs: Galileo insisted on the Platonic idea of circular orbits, Kepler was an astrologer, Newton had some weird alchemical ideas. And many, many important scientists have been devout Christians. That never stopped them from advancing science.

[Keysh]

That the church rejected heliocentrism because it clashed with scripture is a common misinterpretation.

No, it's the simple truth, as the Church and other documents from the time attest.

Galileo's model did not match the observations of the time

Galileo did not have his own model of the heavens; he was a proponent of Copernicus's heliocentric model, which gave predictions approximately as accurate (or inaccurate) as those of the Ptolemaic model. Galileo's observations of the phases of Venus, however, did render the Ptolemaic model untenable, as most astronomers admitted once they had confirmed Galileo's observations themselves. After that, the debate was between heliocentrism and various neo-geocentric models, like Tycho Brahe's.

Galileo may well have offended the Pope with the character of Simplicius, but that character appeared in the book Dialog Concerning the Two World Systems, which was published in 1632. Copernicus's De Revolutionibus was placed on the Index of Prohibited Books, along with other heliocentric texts, 16 years earlier, in 1616. (This was also the time of the Inquisition's first investigation of Galileo, for promulgating doctrines contrary to scripture.)

The official Church decree of 5 March 1616 read, in part: "This Holy Congregation has also learned about the spreading and acceptance by many of the false Pythagorean doctrine, altogether contrary to the Holy Scripture, that the earth moves and the sun is motionless, which is also taught by Nicholaus Copernicus's On the Revolutions of the Heavenly Spheres and by Diego de Zuñiga's On Job. This may be seen from a certain letter published by a certain Carmelite Father, whose title is Letter of the Reverend Father Paolo Foscarini, on the Pythagorean and Copernican Opinion of the Earth's Motion and Sun's Rest and on the New Pythagorean World System (Naples: Lazzaro Scoriggio, 1615), in which the said Father tries to show that the above-mentioned doctrine of the sun's rest at the center of the world and the earth's motion is consonant with the truth and does not contradict Holy Scripture. Therefore, in order that this opinion may not creep any further to the prejudice of Catholic truth, the Congregation has decided that the books by Nicolaus Copernicus (On the Revolutions of the Heavenly Spheres) and Diego de Zuñiga (On Job) be suspended until corrected; but that the book of the Carmelite Father Paolo Antonio Foscarini be completely prohibited and condemned; and that all other books which teach the same be likewise prohibited..."

("Corrected" in this case means with their heliocentric content censored.)

See the following for more of the background: http://copernicus.torun.pl/en/revolution/reception/2/ https://ui.adsabs.harvard.edu/abs/1989JHA....20....1W/abstra...