There's an oxymoron. They should have been excommunicated 300 years ago. That's the Catholic Church's fault for chartering so many orders.
Orthodoxy requires rigid hierarchy.
Ironically, the Jesuits were originally founded with military-style obedience to the Pope and loyalty to Catholic doctrine, and the Jesuit order truly was one of giants.
Obviously they've gone off the rails in the hundreds of years since then, but it's hard to take seriously a claim that they shouldn't have been chartered in the first place.