Rans Enduro Sport, Hase Kettweisel Tandem, Merin Bear Valley beater bike
It's not the quick release. Your wheel is located laterally by the axle locknuts against the frame dropouts.
I'm guessing that you are flipping your bike upside down to install the wheel. If that's the case, it's operator error. Try standing your bike on it's own wheels while you snug up the quick release. That'll make your wheels bottom snugly in the dropouts, the wheel will be nice and straight, and your disc brake won't rub.