Mystery, science and what we retrospectively see as "religion" co_existed. This didn't end in the classical.
Consider the medieval European priesthood... for example. It's basically where all scholarship and literacy resided. Also esoterica, healing magic, astrology, alchemy...
This persists until the scientific age. Mendel was a monk. Newton was highly devout, and mostly devoted to jewish christian protoscience... some of it tracing all the way back to those Egyptians. If you'd asked him, he would have probably described himself as an alchemist.
Recall that the church tried Galileo... because his published results negated Church dogma. That's because the study of celestial motion was a religious function. Always had been.
Ancient Greek philosophers are often seen as "proto-secular." They were mostly seperste from formal priesthood and often treated homeric gods and myth with scepticism.
But... they tended to be highly devoted to "mysteries" and their cults. There's also evidence that Socrates and co taught "secret" esoterica too... about the secret nature of the world... and triangles.
Math, religion, deciphering of celestial patterns.. those have been together for a long time.
Having religion separate from math, physics and natural science is a modern invention.
Copernicus was well liked by the church and so his ideas that Galileo would make more popular weren't a problem originally, Copernicus books were fine for quite a while. The real problem was Galileo was just not well liked and there were all sorts of church issues going on at the time. The church or some aspects would later apologize like 20 years later after the event saying they went too far. Copernicus of course ran into stuff other Greeks and other cultures had seen far before. You make it sound like "Always had been" literally always had been when throughout history it was much debated and even acceptable without issue. I'm not Catholic though so I might get some of their history or terminology a bit mixed up but still. Throughout history various people have debated this topic and I know more about it from my Greek history class by accident then anything - Aristarchus of Samos was well known for debating for it and others following did try to prove it etc. Had the Greeks been more sure and had more proofs the church would have defaulted to that since so much was based on Greek thought but alas, people can only do so much in a time.
Priests weren't (and, I suppose , still aren't) expected to do heavy labor or manage a household, and they had to be literate to perform the Mass and all of the various sacraments. They were all scholars of religion and philosophy by training, and had the free time to persue other studies if they desired. That said, being a priest isn't just a job, it's a 24/7 commitment. Catholic priests had to give up all lands and any possibility of marriage, and especially in the middle ages the performance of various religious ceremonies took up a LOT of time. They also had to actually manage churches as institutions, and churches themselves could own lots of land and have tenants and whole economies under their purview.
Consider the medieval European priesthood... for example. It's basically where all scholarship and literacy resided. Also esoterica, healing magic, astrology, alchemy...
This persists until the scientific age. Mendel was a monk. Newton was highly devout, and mostly devoted to jewish christian protoscience... some of it tracing all the way back to those Egyptians. If you'd asked him, he would have probably described himself as an alchemist.
Recall that the church tried Galileo... because his published results negated Church dogma. That's because the study of celestial motion was a religious function. Always had been.
Ancient Greek philosophers are often seen as "proto-secular." They were mostly seperste from formal priesthood and often treated homeric gods and myth with scepticism.
But... they tended to be highly devoted to "mysteries" and their cults. There's also evidence that Socrates and co taught "secret" esoterica too... about the secret nature of the world... and triangles.
Math, religion, deciphering of celestial patterns.. those have been together for a long time.
Having religion separate from math, physics and natural science is a modern invention.