Since Templars are said to have started with nine members I'd venture to say they've been corrupt from the very inception - see Ennead and ONA (Order of Nine Angles or Angels rather).
Hospitallers had a beef with Templars but I don't know if that was just a trivial power struggle (or a show) like English vs French masonry or nazis vs commies. Whatever the case Hospitallers - Knigths of Malta are the same occult shit now. Curiously enough Malta is an island with a very intriguing area in terms of megalithic structures and legends of giants.
Not very familiar with Livonian Order but since it fell under Teutonic Order I can only tell you it couldn't have been on the side of good. Teutonic Knights were just a medieval attempt at drang nach osten under the guise of spreading christendom and veiled in deviously crafty diplomacy. Slaughter, rape, pillage didn't matter as long as it was against heathens lol.

It's naive to expect a force of good in the world of darkness that should defeat the darkness by employing the ways of the darkness it seeks to overthrow. Only thing that could've helped would be genuine biblical Christianity since it addresses the core problem but the stage is already set for widespread persecution even in the so called civilized countries so it won't be a solution you perhaps hope for. But a solution is not possible.

World has to fall for people to understand that even at their highest wit they're foolish and, despite utmost efforts, helpless. I'm not talking about the Great Reset here but another attempt at a golden age that comes later with a promise of solving all the ills of this world but will end up a nightmare.