Was Copernicus overtly persecuted by the Church? No - but he certainly understood the cost of going against the Church. The history of the the publication of Copernicus'
De Revolutionibus grants us some insight into the danger of daring to publish anything contrary to Church ortodoxy. In this case, Copernicus' own introductory letter was substituted for one that disclaimed the merit of the work. The editor, until recently, was accused of excessive piety for not wanting to offend the church; now it is believed that he cleverly included the preface knowing full well that sophisticated readers would understand the necessity of the disclaimer merely as a ploy to get it past the church censors and into print. Galileo used something of the same device to get
Discourses into print. He set up straw men who argued against his theories but who in the end had to concede their correctness.
So, in a very real sense, Copernicus escaped religious persecution by dying before the publication of his work.
And let us note that some sixty years later, Giordano Bruno was burned at the stake for espousing Copernicus’ cosmological theory, and that later Galileo himself was convicted of heresy for the same crime. Galileo officially recanted his work, but never truly gave it up.
You state that the Church can and has thrived in many different socio-political-intellectual milieux - this much is true. History has clearly shown us that where the Christinaity in general and in particular, the Catholic branch has erred, it has always been in the pursuit of unbridled power and the corruption that accompanies such pursuits. Christianity's great strength is that, unlike Islam, it has and will continue to reform itself.
You misrepresent the case of Copernicus whose theory was mainly a revival of an old Greek cosmology. It was “dangerous” primarily not because of any religious heterodoxy but because it went against the scholarship of the day—A bit like the ID position in the matter of evolution, it could be regarded with suspicion by all in authority. Copernicus himself proposed his version of this theory because of the difficulties with Ptolemy’s theory arising from new observations. However, his theory was flawed because it supposed that the planets moved around the sun in circles. It was not until Kepler’s work that the heliocentric system was made compatible with the data. Galileo got in trouble with the Church authorities when he pushed the envelop of acceptance. He had been told to present his theory as hypothesis; he insistence of arguing that it was absolutely certain. But as his proof was geometrical in character, and certainly was generally expressed in terms of Aristotelean physics, his reasoning found no acceptance. It was untimely, as Einstein’s theory of relativity would have been if he had proposed it before the Michaleson-Morley experiment disproved the ether theory. Galileo displayed the typical arrogance of genius, and it get him into deep trouble.
As for Bruno, he was deep into mysticism and insisted on holding to some wild theories, including multiple universes. Dangerous stuff in the midst of
religious wars that were tearing nations apart.