Your orthodontist can give you hints and tips to help you continue with your favourite hobbies.
For playing sport it is most likely a mouth guard of some sort will be needed. Talk with your orthodontist about the right protective mouth guard for the sport being played. In the majority of cases, patients can continue playing their sport of choice. Your orthodontist or general dentist can advise regarding fitted a mouthguard during braces treatment. Prevention of mouth injuries is extremely important.
Regarding playing musical instruments, it may take a week or two to get used to playing with braces, but most people soon forget they are wearing them when playing! There are protective devices available to assist with some musical instruments. Please ask your orthodontist for more information.