Galileo was educated in part in a monastery and at the Uni of Pisa (founded by a pope). He was sponsored by the Church to do his studies; when he wished to publish his pamphlet the authorities urged caution and refused to state outright that heliocentrism were true wishing instead to gather more evidence. Galileo went ahead pissed off the papacy and was censured.

Indeed if we consider Einsteins relativity then we might argue that the anti's were right to hold reservations as without an ether it is no more correct to say that the Earth revolves around the Sun than it is to say the Earth is static. I doubt they had this in mind though.