I'd attempt to answer this by comparison.

Clement VII (IIRC) himself had attended Copernican lectures, and the Cardinal of Capua sent him a letter, saying:

I have also learned that you have written an exposition of this whole system of astronomy, and have computed the planetary motions and set them down in tables, to the greatest admiration of all. Therefore with the utmost earnestness I entreat you, most learned sir, unless I inconvenience you, to communicate this discovery of yours to scholars, and at the earliest possible moment to send me your writings on the sphere of the universe together with the tables and whatever else you have that is relevant to this subject.

Copernicus also had extensive communication with, and dedicated De revolutionibus orbium coelestium to Pope Paul III. This is Copernicus, who is practically responsible for modern heliocentrism.

Kepler was publishing as a practicing Lutheran in the court of the Holy Roman Empire. And he even wrote a treatise explicitly supporting Galileo's Sidereus. The Emperor Rudolph II was a very fond patron of Kepler, and his successor even kept him on the payroll despite some scandal in Kepler's own life.

Clearly, Galileo is the odd man out in the heliocentrist community. His arrest was definitely more about his theological-political leanings than his theoretical ones.