I think you should definitely just apply and give it a shot! Depending how you rate certain areas, there's a chance you'll get placed in that type of job in the program if you make it in so make sure you put 0 or however the rating is for that section if you're absolutely not interested in it because even if you put like a 1 or something, there's a chance they'll put you in that kind of job. If you get through to the phone interview step, that's where you will definitely make your mark! They're really friendly so just deep breaths and be you, make some jokes or something, they'll definitely love it! lol
I know people that were a bit introverted and did the program and it honestly really opened them up from their shells since you have to interact with guests and such but it's in a friendly, happy environment to do that so it's a great way to work on that part of yourself it that's what your parents were referring to, especially if it's in something that you love (disney), then it'll only make it that much easier. I think the program can be a really great experience and opportunity so if you really want to do it, apply and see how things go!