They are the largest Catholic religious order and you will find very conservative Jesuit institutions like Ignatius Press and St Louis U ad liberal ones like Georgetown. They simply reflect differences in the Catholic Church at large.
I'm pretty sure that the Franciscan family far outnumbers the Society of Jesus. Furthermore, they don't simply reflect the diversity of the Catholic Church. The fact is that a large portion of the Society got very heavily into Liberation Theology several decades ago and they are still reaping the rotten fruits of that exploration. While much of what has taken place at Jesuit Universities cannot be blamed on them as in many cases they are no longer really in control, some can
be blamed on them as well. As noted above, there are
several faithful and orthodox Jesuits, some of whom have already been mentioned. You could also add men such as Fr. John Hardon, Fr. Kenneth Baker, Fr. David Meconi, etc. I am sure there are many others living their vacation faithfully without making any sort of waves at all. However, there are also many who have gone off the path. In 2008 at their General Congress, Pope Benedict called them to task a bit and told them what he wanted from them. After taking his words under consideration, they responded with this document in 2010. http://www.sjweb.info/35/documents/decrees.pdf
Peace of Christ,