Lick My Frosting
Join Date: May 2008
Location: Milton Keynes, UK
Thinking about it, I think any form of Boxing or Muay Thai would be risky as of course, braces creates a lot of tension between you teeth to realign them. Any form of impact could be undoing the good work your braces are doing of keeping your teeth in the right place.
BJJ should be fine, but you don't want direct impact straight on your teeth. Mouthguards for braces are available (Google) but even then...it's a risky move.
My personal opinion of course.