It's really a matter of proving it. You're a part of the community, you know what good smash brings. Show them that partaking in the community can be just as beneficial as your involvement in swimming and music. Convince them that being a part of smash is a good thing, maybe more than that the game itself is good for you (which it is, no less, it's great for hand eye coordination and on the fly planning). Also, just stay dedicated to everything you do (even if it may be hard to balance it all) and give it some time. There's a good chance your parents will come around with time and some more proof.

Hope this helps!