Oh, it can be done! I'm not one of those lucky or talented enough to have a serious musical career alongside flying, but I do know many that do - and I play at it.
The problem is that certain periods in each career need 100% concentration. If you time things well, you can progress in both careers without overly affecting the other - but if you time things badly (and who has control over these things?) one or both careers could fall apart! I guess the secret is prioritisation. Aviation is intolerant of lack of application, and will spit you out if you don't continually make the grade. Music can be more forgiving.
If you're unsure which to prioritise, I'd choose aviation. After you get the all-important qualifications, you can loosen up a bit. You can practice music almost any time; you don't need a formal organisation to do it. You most certainly do in flying! But what do I know?
Bruce is probably the exception that proves the rule, along with our own £6: professional airline pilots are not generally professional musicians. Airline pilots tend to like structure, predictability, order etc. Musicians (rock'n'roll, at least) are less easily pigeonholed. If you feel that creativity and freedom to make music are more important than flying aeroplanes (and why shouldn't they be), then make music your no. 1. If you're more disposed to the opposite, then piloting may be the way ahead. Tom Petty and Dave (call me David) Gilmour are examples you could study.
The thing is, flying and music are not mutually exclusive. They may need prioritising one way or the other from time to time, and your personal feelings will determine which way is your own priority. Be assured, they are not incompatible - you just have to find a way they work together for you!
Best of luck!