The more important differences

It is the intellectual atmosphere which is toxic rather than the physical atmosphere however there really isn't anyone else who can survey the entire historical and technical picture and identify why such destructive ideologies emerged over the centuries and why they have now become particularly offensive.

The most difficult tangle is at the juncture where geocentricity meets heliocentricity and the intricate if not tangled issues which divide proof of the Earth's motion through space from the predictive facility which uses days and the calendar system to determine astronomical events. Some times contemporary commentators come close ,at least in presenting the difficulties but of course can only go so far -

"Since the time of the Greeks, the purpose of astronomy was to “save the appearances� of celestial phenomena. This famous phrase is usually taken to mean the resorting to desperate expedients to “save� or rescue the Ptolemaic system. But it meant no such thing. To the Greek and medieval mind, science was a kind of formalism, a means of coordinating data, which had no bearing on the ultimate reality of things. Different mathematical devices—such as the Ptolemaic cycles—could be advanced to predict the movements of the planets, and it was of no concern to the medieval astronomer whether such devices touched on the actual physical truth. The point was to give order to complicated data, and all that mattered was which hypothesis (a key word in the Galileo affair) was the simplest and most convenient. " Notes on the Galileo Affair

Copernicus would have tried to fit his system into the antecedent geocentric data but it can't and should not have been done as the perspectives which work for the outer planets cannot be used for the inner planets so there is no one-size-fits-all view which combines all the planets of the solar system.

The empiricists exploited the unresolved issues and reworked the Copernican discovery into a narrative which is wildly adrift of discovery which uses the Earth's motions to account for so many observed effects on the surface of the Earth, accounting for the motions of the planets ,including ours, around the central and stationary Sun -

https://en.wikipedia.org/wiki/Copernican_principle


The vast majority here have their own thing going on at their own levels of comprehension however there would also be a number who are not entirely comfortable with the ideology they inherited .

The fascinating clash between heliocentric and geocentric astronomy was always going to happen and not because of some imagined Church ideology that required the Earth to be stationary and central but rather how to reconcile the facility which predicts astronomical events on one side with observational proof that the Earth moves through space and around the Sun. Our era should be neither prisoners nor exploiters of this history as the relationship between planetary dynamics and terrestrial sciences take priority over the ancient methods and perspectives.

The stranglehold of a geocentric framework which overlapped heliocentric reasoning has been obliterated by partitioning perspectives between the inner and outer planets whereas the original heliocentric astronomers worked off a single framework where all motions were gauged against a stationary stellar background, it works great for the outer planets but not the inner planets.

A further complication has also been removed as the late 17th century people tried to model the solar system using timekeeping without due care or consideration. So where to begin ?, appeal to contemporaries to revisit the original foundations of their clockwork solar system ideology ?, appeal to the original insights which distinguished geocentric reasoning from that of a moving Earth ? or just simply deal with the relationship between terrestrial sciences and planetary dynamics using visual tools and then fill in the details of everything else later.

The last option is preferable as there is enough creative ground to advance priorities for our era while acknowledging the past for good or otherwise.

In astronomy the idea of hypothesis,at least in geocentric astronomy , was accounting for the observed motions and it didn't matter whether the modeling was physically true or not , as long as it fitted in with observations. This view was extended by Kepler and even though I wouldn't be a great fan , his matter-of-fact statement is consistent with his approach to relative motions between the Earth and the other planets -

"And though some disparate astronomical hypotheses may provide exactly the same results in astronomy, as Rothmann claimed in his letters to Lord Tycho of his own mutation of the Copernican system,nevertheless there is often a difference between the conclusions because of some physical consideration...But practitioners are not always in the habit of taking account of that diversity in physical matters. " Kepler


Modeling has been a component of astronomy for many thousands of years however the emergence of heliocentric reasoning changed all that. Even though Copernicus tried to rework his insights back into geocentric observations, these observations contained a problem which makes such an attempt impossible.

Followers of modeling including those who model the Earth's motions via a rotating celestial sphere (RA/Dec) may not have the intuitive sense to determine why cause and effect between the Earth's motions and terrestrial sciences takes priority leaving the perspectives for solar system structure using the relative position to the outer and inner planets as a secondary pursuit,at least for the time being.