Classical rebels?

Wow, old classical that's outside the box... Well, Bach was a bit of a renegade man in his time. It's hard to think of anything from that far back as rebellious, as it typically became the norm before too long...

in the days before the French revolution changed politics forever, aristocratic patronage dominated music, and getting along with wealthy individual sponsors was pivotal for a composer (as it was, by the way, for writers, philosophers, etc). also, composers often held positions as music directors at a court, or in a large church, serious regular duties. it's only with the rise of a cult of "genius" that composers could get away with rebellious lifestyles. of course, if you mean rebellion in their musical aesthetics, that's something else; and often a renegade person writes mainstream music while a mainstream citizen could write rebellious music.

Shosty wasn't all that outside the box, though... Try some Bartok or Hindemith if you want modern outside the box. Like I said, though, really old stuff that deviated too much from the norm has been largely forgotten...

as an example of a long-ago composer really bending rules and ears, go back to GESUALDO - just recently heard some of his works performed alongside with works written in the last decades of the 20th century, and oh boy, awesome stuff.

as an example of a composer living rebelliously, with contempt for good behaviour, look no further than potty-mouthed, libido-driven MOZART!

Mozart. 

He most likely meant the 1947 John Adams, Nixon in China was... something.

Nice Gesualdo reference!  Getting into the Romantic Period, Paganini (1782-1840) definitely fits the bill.  He achieved rock-star status with his virtuosic violin performances and his extreme promiscuity.  Based on the lifestyle he lived and the fact that he could do things on the violin that nobody thought were possible, rumors started to spread around that he was the devil himself.  Doesn't get much more death metal than that.

20th century fave: Gyorgy Ligeti.

Earlier and more radical than any of the "minimalist" types, I think.  His range is too great for  him to be pigeonholed, though, so harder to market.  I listen to (*extremely short*) choral piece, "Lux Aeterna", and can't believe it's not electronic music, every time.  Stunningly beautiful, too. HIs work for metronomes might be a little harder to get to...

But limiting to 15-18th centuries, maybe Biber.  17th century guy.  Some really stunning and radical music for strings.

And going back to Tudor England, there was William Byrd, who was both the court composer for Henry VIII, writing large-scale music for the Church of England, and a secret Catholic at a time it would cost his head, writing smaller pieces to be sung in Latin -- smaller so they could disperse in a hurry should they be in danger of getting caught singing.  That's a radical.  The motets are the smaller/latin pieces, and some really gorgeous stuff.

John Cage.

Charles Ives?