My husband and I are both Loyola Maryland alums. And our S21 has applied EA. Loyola Maryland is his top choice. We are trying to be all chill about that. Really. I swear. 
First, to clarify what @TS0104 said above, Jesuit colleges are Catholic colleges. Jesuits are an order of Catholic priests who have historically focused on service and education. The current pope is a Jesuit (the first one from the order to be pope) and he is causing a bit of controversy by expressing what some more conservative Catholics consider to be “liberal” views.
The thing about Catholic colleges (even the more liberal Jesuit ones) is that they often attract Catholic-identifying students, who can be on all points of the liberal/conservative scale. So you often have a mix of viewpoints on campus. Perhaps this is where the conservative thing comes from.
Jesuit schools all hold the same values and mission. However, Loyola Chicago is also significantly larger than Loyola Maryland and in a much larger city. But we’re talking about Niche. So, I wouldn’t really worry about it.