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Johann Widmanstetter was a proponent of Copernicanism and a secretary to Popes Clement VII and Paul III. He explained the theory to Clement VII, presumably in the terms that we find in the preface to the Revolutionibus, which assert its purely mathematical nature. Clement was pleased, but died in 1534, and the work was dedicated to his successor, Paul III.

If the work was nothing but an ornament to these Popes, Copernicus and his functionaries worried a great deal about its reception by the Church. It's a long and well known story, with the finished work and its apologetic preface coming into Copernicus' hands the very day he died.

It was fifteen Popes later, under Urban VIII, that Galileo received his sentence of condemnation:

We say, pronounce, sentence, and declare that you, the said Galileo, by reason of the matters adduced in trial, and confessed by you as above, have rendered yourself in the judgement of this Holy Office vehemently suspected of heresy, namely of having believed and held the doctrine which is false and contrary to the sacred and divine Scriptures - that the Sun is the center of the world and does not move from east to west and that the Earth moves and is not the center of the world; ...

Apparently Urban VI was more or less indifferent to heliocentricism. He was a friend of Galileo and had read a draft of Dialogues and asked Galileo some questions about the treatment of tides. Galileo told him he would clear it up in the final edition He did so by putting the Pope's questions in the mouth of the character Simplicus, only to have them swatted away dismissively by the character of the wise Salvati. Galileo was like that. He had an abrasive personality and a talent for making enemies. What is worse, is that he had absolutely no idea about the mechanism of tides, had never really studied them and just talking smack. It would take Newton and his disciples (mainly LaPlace) about 100 years to come up with a reasonable explanation of tides.

Dialogues gave Galileo's enemies a pretext and they seized it. His former friend, the Pope, did nothing to help him, though it is unlikely he would have without the insult Galileo had given him in Dialogues.

Copernicus' literary agent, the Lutheran cleric, Andreas Osiander, inserted the following unattributed preface to De revolutionibus:

"Beware if you seek truth in astronomy, lest you leave this book a greater fool than when you came to it."

It was an attempt to ward off eccliastical wrath. While the Church was indifferent to heliocentricism, Luther personally believed it to be heresey and was violently opposed to it at the time of publication. Osiander also placed in the disclaimer that helocentricism was only an "hypothesis", what we today would call a mathematical model and did not represent reality. Copernicus only saw the final edition on his death bed and he was outraged by Osiander's insertions. Copernicus thought he had discovered the truth, that the planets did revolve around the sun, but by that time there was nothing he could about it.