Will I be held responsible for working with a supervisor accused of sexual misconduct?
The matter is best left to the official circles. Do not pry, do not gossip. As for being tainted, you are just a student and dependant, and if you neither enabled nor profited from the prof's (alleged, we don't know) misconduct, you should be fine. But if you start poking your nose into matters yourself, you'll get into a lot of trouble, from being seen as a nuisance to the officials, to getting the prof upset, to violating privacy laws, to unwittingly becoming a witness.
A career-limiting move.