You are quite correct. Neither the parish nor the high school of St. Francis Xavier come under the authority of Cardinal Dolan. They are under the authority of the Jesuit Province of NY State.I would assume the same for St. Francis of Assisi on 32nd Street. They would fall under the authority of the Franciscan Friars Minor. Xavier has for a long time been very welcoming of the homosexual community. My brother in law and his partner when they would have the family for Christmas Eve would attend services there as they lived about a half mile away. Even though I am a graduate of Xavier HS my wife and daughter and I would attend services at Epiphany parish on 2nd Avenue instead.
Sorry you are wrong. A Catholic bishop gives the final imprimatur to any activity in his diocese. If he deems an activity, community within his jurisdiction as contrary to church teaching or dogma, it is his duty to take definitive action. The Bishops have been reluctant to discipline the Jesuits. Suspect that the Jesuits know quite a bit about the dirty laundry n each diocese and would not be hesitant to share the information with the press or prosecutors if they feel threatened. The Jesuits have devolved into an unspeakable cabal. The biggest fraud is when hard pressed Catholic parents send their children to today’s Jesuit schools and assume they will receive a Catholic education.