According to a quick Google search, Copernicus published his “heliocentric theory of the universe” theory the year he died in 1543. Did he withhold his theory until he thought he was close to death knowing it would be controversial?
It’s complicated.
One examination of the subject is found in Mano Singham’s “The Copernican Myths” published in Physics Today.
He argues that the Catholic Church had no doctrinal objections, and in fact taught the book at first. But Martin Luther spoke out against heliocentrism and so Protestant churches condemned the book. Over time, their viewpoint became dominant and spread to Catholic countries. It was placed on the Index of Prohibited Books in 1616.
However, the book itself contains an introduction dedicated to Pope Paul III that carefully tiptoes around objections by mentioning prominent Catholic figures who, he claims, had long urged him to publish.
No doubt there’s a conflation of later prohibitions with the initial reactions. Nevertheless, Copernicus was well enough acquainted with contemporary religious thought that he knew the problematic notions that he was espousing could be used against him. We can’t be sure of his exact mental processes, to be sure. All we know is that he took the safer route.
Much of the later religious objections resulted from the fact that Galileo was a dick (pro tip: When your patron gives you his blessing to publish a book, don’t name the character based on him “Simplicius”, and make him wrong about absolutely everything). Copernicus died before Galileo took up the idea, so it would have been much less of a problem for Copernicus.
But “much less” is not the same thing as “no problem”, and waiting to publish until you’re dying certainly avoids some difficulties.
That particular book was published in 1632, so it couldn’t have been the cause for Copernicus’s book being banned in 1616.
Galileo’s findings were instrumental in the argument for heliocentrism, of course, but the Church was already adamantly opposed to considering it long before Simplicius ever saw print.
But the Church wasn’t adamantly opposed to considering it. When Galileo asked the Pope if he could write a book comparing the two models, the Pope said yes (without realizing how much of a hatchet job it would turn out to be).