I was not surprised by this, because I know many Catholics honestly try to be rational... of course only within the limits given by the Church.

They would have absolutely no problem with Bayesian updating; the only problem would be the Solomonoff prior. If you replace it by "the Catholic Church is always right" prior, you are free to update rationally on everything else and remain a good Catholic.

This is why Catholics don't have a problem to accept e.g. evolution, as long as someone can provide an explanation how evolution can be compatible with "the Catholic Church is always right". (A possible explanation could be e.g. that God created the first life forms; that evolution is a consequence of physical laws created by God, therefore any result of evolution is still indirectly created by God; and that humans are somehow an exception to this process, because even if their bodies are a result of evolution, they also have an immaterial soul created directly by God.)