The issue of underage characters also comes up in the World of Darkness. Canonically, Garou first changes hit with puberty, so your typical CG-level Cliath should be around 16 years old.
That can be fine in a movie, or a book, or in tabletop play. But on a MUSH it just gets ruined by the minority.
So I think you just have to adapt the setting to fit the needs of a MUSH. Stretch it, change it, rewrite it. Or House Rule things. Or anything.
If your setting can’t be adapted, it won’t work as a public MUSH.
In the case of Star Wars, yeah, it was stated canonically that kids started Jedi training very young. But they were started as initiates, and then became younglings (the younglings!). By the time they reached Padawan status not all were teenagers anymore, even. So even if you want Padawan PCs, they can still be required 18+ and not even stretch the setting.