It is unfair to tie Flat Earth, or any pseudoscience, to “traditional Catholicism” in particular. Some people who accept pseudoscience also happen to be traditional Catholics. Many flat earthers, or other pseudoscience followers since the Reformation happen to be fundamentalist Protestants (not fair to identify Protestants with this few, either).
The classic analysis of pseudoscience, including Flat Earthers, was “Fads and Fallacies in the Name of Science”, 1957, by Martin Gardner. However Gardner later wrote followup books and articles about the pseudoscience associated with the developing New Age Movement, whose adherents are far removed from any kind of traditional Catholic or Protestantism.
Gardner was a theist, who strongly admired G. K. Chesterton and H. G. Wells. Had he lived a little later, I think he might have become Catholic. It is more apparent that Wells’ rejection of Christianity as supposedly Faith triumphant over Reason was increasingly inaccurate, and that Chesterton’s respect for the Church as the defender of Reason fits the current reality.
I wonder what Gardner would say about the current attack on Reason and free speech on our campuses, if he were alive now. They aren’t making fair minded, objective skeptics like Gardner anymore.