Nobody seriously expects that Disney's customers will boycott over this. If they suffer any fallout at all (which I doubt), it won't be from the consumer side. It will be the chilling effect this story has on new hiring. If more skilled workers think twice before accepting a job with Disney, it could inconvenience them in the future.
Even that worst-case scenario is pretty mild, so you can expect Disney to put do a little bit of spin control on the story and then forget about it.