Pseudoscience involved drawing conclusions based on a few facts, ignoring many other more relevant facts. It was not pseudoscience for some ancient people to believe in the flat earth, because the evidence then was mixed. It is pseudoscience to ignore the evidence since then. Wilbur Voliva, 1870 - 1942, a Protestant evangelist, was perhaps the last prominent religious person to push this theory.
Most pseudoscience today is secular in origin, especially related to the New Age Movement. It flourishes because we are moving into an anti-Reason age; I fear the next step may be a Dark Age. Reason is not the enemy of Christianity; Christianity may be the last defender of Reason.
I know one “trad Catholic” website periodically pushes the idea that maybe, just maybe, the sun does go around the Earth. (Hey, all we’re saying is, let’s be open minded about this). They are willing - no, excited - to challenge the scientific establishment, just as they challenge the Church establishment. They seem to do this whenever their website hits or donations start dropping. The religious Far Left is even more anti-Reason.
Chesterton: “An open mind is really a mark of foolishness, like an open mouth. Mouths and minds were made to shut; they were made to open only in order to shut.” (Illustrated London News. October 10, 1908)