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.
I completely forgot what braces actually do when I gave my opinion, wow. I think Liza is correct here, with all that tension it really isn't worth the risk.
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