They were said to have influence and educated the sons of the richest European families. A lot of people find it strange when you point out the influence Catholics have in the CIA for example, saying that there's millions of them everywhere, but while not every single person who comes from those universities or who is a Catholic could be an agent, the Roman Catholic Church as an institution and the Jesuits are one and the same. It was thanks to the efforts of the church that national socialist officers were able to get away and they contributed in creating the CIA and according to a lot of authors, the CIA has been run by Catholic elitists for a long time.

Even if you ignore that, the Jezzies themselves have admitted their many plots with their own media many times over, yet when you point out how the Catholic Church could be behind a certain plot, most people can't deal with it.

I think the truth is simply way too terrifying like for them to hold themselves together.