Copernicus – whose day job was Roman Catholic church canon in what is today Poland – had published his main work, De revolutionibus, in which he proposed that the Sun was at the centre of the solar system, in 1543, and his ideas were openly discussed and reasonably well-received even by the Church at the time. Towards the end of the 16th century, his book actually became required reading at various Catholic universities. It took the Catholic Church until the “Galileo affair” 70+ years later to do something about De revolutionibus: In 1616, a decree was issued saying that the book should be changed to stress that what it proposed was a mere idle hypothesis and speculation, and to avoid the impression that it attempted to describe the actual world. (The original, uncensored version remained on the index of prohibited books until 1835.)
One reason for this is that Copernicus’s ideas, while revolutionary, were not a huge practical improvement on the prevailing theories at the time (Copernicus’s solar system was still based on circular orbits with epicycles, like the traditional Ptolemaic system and the more modern one put forward by the Danish court astronomer, Tycho Brahe), so it was easy to shrug them off as fanciful, unscientific, and unnecessary. It did take the efforts of Galileo, Kepler, and finally Newton to establish the heliocentric system as clearly superior to the previous ones, at which point the Catholic Church had bigger fish to fry. (In fairness it should also be said that the Protestant churches at the time weren’t too hot on Copernicus and his ideas, either. The great man himself was not personally affected by all the controversy, though, having died very shortly after the first copies of De revolutionibus had come back from the printer.)