Catholics didn't have any issue with Gutenberg. In fact it was exactly the opposite. Please check a letter from Enea Silvio Piccolomini (future Pope Pius II) where he expressed his feelings on how great Gutenberg invention was, how clean was the print, etc. - https://www.bavarikon.de/object/bav:BSB-CMS-0000000000004546...
OP may be thinking of Tyndale. He printed the Bible in English for the first time, making it accessible to a much broader range of people. (Gutenberg's was in Latin). That together with the fact that he was executed for heresy leads to an often repeated "Catholic Church didn't like printing press" narrative, but it's oversimplified and unfair. Tyndall was in the thick of the Protestant Reformation, and his execution had to do with his unwillingness to recant certain theological positions and apparently not much to do with the printing.
It remains an excellent example of free information causing chaos in society. The cost of transitioning Europe away from Catholic hegemony - in which widely available English Bibles was certainly a major force - was at least a few centuries of conflict and war, some of which still isn't entirely settled after 500 years. Power transitions, historically speaking, tend to be messy and involve wars. Our own information revolution is not less disruptive than the printing press - I would say maybe more so. So it shouldn't surprise us if we're in for troubled times while things shake out. It is easy to accuse old power of refusing to give it up, and that isn't wrong, but also sometimes that old power was the only thing doing the job of keeping chaos at bay.
Interestingly, the first printed German bible translation appeared in 1466 by Mentelin[1,2], only 11 years after Gutenberg's Latin bible. Luther's[3] and Tyndale's[4] influential translations only happened 50-60 years after that.
