From my understanding, personality rights laws are like trademark laws. If a trademark is used without permission for monetary gain, it is considered illegal. The same can be said with likeness/voice/character of a person unless it falls under parody purposes which is completely different.
The key here is "used without permission". If the actor signs a contract they essentially are giving that permission. You can't simply just decide one day to back out. They can try to file a lawsuit, and if Disney still wanted to pursue it they can counter sue for breach of contract. Ultimately a judge would have to decide which law takes precedence over the other. It all depends on if the court fees and time were worth it in the end to either party involved.
I really have no clue as to what's going on with the topic at hand. I don't know if the show is already made and if contracts have been signed. I just wanted to point out that personality rights don't automatically overrule contractual agreements......at least not without a court ruling.
To address this line specifically: "So just because it’s already recorded doesn’t automatically give Disney the rights to use it, especially since it hasn’t been release yet," there is no way Disney would start a recording session with an actor without contracts being hashed out beforehand. That would be bad business and Disney isn't new to the rodeo here. If the actors gave permission through contract (and the contract very specifically didn't say they can't use the likeness, which is possible, but unlikely), then yes, Disney has every right to use it......just as the actor has every right to try and fight it. It's not as if Disney is grabbing random sound bites from the actors' public appearances and using them for their show. The actors signed contracts, willingly stepped into the studio under those contracts, thus giving permission. The same goes with using clips from movies (again, unless their movie contracts specifically said their likeness in those clips can't be used, which again is unlikely).