'Fashion Police' Staffers -- Giuliana Rancic and Kelly Osbourne Are Ruining Joan Rivers' Legacy

Giuliana Rancic and Kelly Osbourne's battle at "Fashion Police" is tearing down everything Joan Rivers built -- at least that's how show staffers feel ... TMZ has learned.

Sources close to the production tell us producers fear the uproar over the Zendaya joke will cause Giuliana to be more silent on the show -- because she'll be worried about further backlash.

We're told producers are worried the other show hosts will follow suit ... and it will no longer be the sassy show full of sarcastic humor that it used to be. They also wish both women had chilled after the on air apology ... because things would have blown over.

We're told Melissa Rivers is now doing everything in her power behind the scenes to keep her mom's legacy alive.