Welcome to the Disboards! I wish I really had some advice for you, but let me give it a try. We haven't "broken" the idea to our parents yet, but I think they will accept it. I am (a little) older and a wedding in any form has been a long time coming, so I think as long as it makes me happy my parents will be ok. Plus my friends and family all know what a Disney freak I am!!! But the actual Disney wedding idea came from my DBF (DF2B! We've been doing planning but I'm still waiting for the ring).
You need to show them how affordable a Disney wedding can be. There are options for all different price ranges: intimates, bare-bones customs, or customs with lots of extras!!!
If you can catch the DFTW episode on the Food Network, or the planning DVD from DFTW...you can show them how beautiful and breathtaking it can be. You can also show the options on the DFTW website, but just know that the prices may not be completely accurate. I believe they list very high-end things on the website. The pictures are beautiful and you can sign-up for a wishbook where it'll give you an <idea> of your budget. But like I said, you can do similar things for less $$$.
Hope that helps!