Remove protective coating quickly
Since it sounds like the film is disintegrating when you try to peel it:
Tape the whole surface, peel the tape (and film) off. You'll need a tape with an adhesive that's more stubborn that the film-to-cabinet bond. I'd probably start with plain old packing tape - fairly strong, usually has good adhesive, inexpensive, can be had wide. But you may need to experiment to find the best tape for the job.
Using a roller on the tape after application and before attempting to peel may help to achieve a better/more uniform bond to the film.