There are MANY Jesuits who are also Catholics. They don’t get the headlines, but they do exist.
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Fr. Mitch Pacwa is a Jesuit who also seems to be an Orthodox Catholic, as well as a conservative American (although he may be a bit conflicted when it comes to his Jesuit brother, this Pope). (I think Fr. Mitch listens to Rush Limbaugh quite often, based on some of the things he talks about, and when he talks about them, in his homilies and his shows on EWTN.)