I find this assertion to be overly simplistic and frankly vague. To be more specific, the primary source of conflict between Pope JPII and the Jesuits was over “liberation theology” in Latin America.
The pope, having lived in communist Poland, was an ardent anti-communist and he perceived liberation theology as being infected with Marxism. Because many prominent Jesuits supported liberation theology, they found themselves at odds with Pope John Paul II. Father Ernesto Cardenal, a Jesuit priest and Sandinista, was publicly rebuked by JPII.
Which side one sympathizes with will obviously depend largely on his or her political beliefs. However, the friction between the Jesuit order and Pope John Paul II was not, shall we say, merely abstract.
Frankly, I do not think this has much bearing on attending a Jesuit college. Some Jesuits might be perceived as leaning left, but others seem more on the right. Besides, liberation theology is no longer a hot issue and even Ernesto Cardenal is no longer a Sandinista.