Popular explanations often mention that the "Catholic Church" had a problem with Copernicus and his heliocentric theory, neglecting that even a scientific disagreement at that period would likely have occurred within the Catholic Church. What were the different responses based on different aspects of the theory? Some of the different viewpoints I seek include Catholic theology, Protestant theology, math, astronomy, and philosophy.
It is a long and complicated story, but a very brief outline is the following. Copernicus book was published in 1543. For about 70 years after that the Church did not express any "official opinion" on it. The book was discussed by several writers, some supported and others criticized the theory, as it usually happens with scientific theories. The church did not interfere.
Some modern popular writers claim that Giordano Bruno was prosecuted as a follower of heliocentric theory. This is not so. You can see in Wikipedia what was incriminated to Bruno. All these items have nothing to do with astronomy or science.
Copernican theory was taught in some universities in the late 1500's, for example in the university of Rostock.
The "political controversy" actually started in Galileo time. This is also a very complicated story, but the result was an official interference of Vatican, a process of Galileo, and the "ban" of several books in 1616.
The book of Foscarini attempting to show that Copernicus theory does not contradict the Bible was banned. The book of Copernicus himself was not banned but had to be "amended". The position of the Church was that heliocentrism is fine "as a pure mathematical theory", but at the same time discussion of its relation to theology was explicitly banned.
One of the books of Kepler was banned (by Catholic Church). Few years later Galileo disobeyed the orders and was prosecuted.
Good source: Stillman Drake, Galileo at work, Dover, NY, 1978.
EDIT. Here are some more opinions. M. Luther: "...fool who wanted to turn the art of astronomy on its head". F. Vieta (famous French mathematician, inventor of modern algebraic notation): "he was the paraphraser of Ptolemy and more a master of the dice than of the (mathematical) profession".
One of the very few people who really understood the matter, Tycho Brahe, admired Copernicus, praised his work, and called him the "second Ptolemy", but also criticised his work and had his own competing "system of the world". Unlike the others, he understood what he was talking about.
Source: A. Blair, Tycho Brahe's critique of Copernicus, Journal of the History of Ideas, Vol. 51, No. 3, 355-377.