Burke is the head of the Human Dignity Institute and he is the only American prelate who is on the board.  No one other than Burke would know what Breitbart was or who Bannon was, especially in 2014.  Breitbart tends to anti-Catholicism but they do shill for Burke quite a bit.  And I suspect that there are connections between Breitbart and Lifesite News/ Lepanto Institute. 

As for Pope Francis, I agree with you that he isn't liberal.  But there is no doubt that he is on the side of the poor and the refugees.  Bannon and the alt right's hatred of Pope Francis has to do with his advocacy for tolerance and inclusion.