They aren't rejected because of their physical forms, they're rejected because they're different. The Us vs Them paradigm. Now, they might be treated better than non-transformed monsters, the same way light-skinned blacks used to be treated better by whites pre-civil rights, but if it was common knowledge there would still definitely be discrimination.
So, could it all be kept a secret? Possibly, but everyone involved would have to be on board and have the discipline not to slip up and reveal anything. They ex-monsters would have to learn to live, talk, eat, etc like mewmans. I'm not saying it's impossible, just that it wouldn't be an easy, simple fix,