Music is a human expression. If a musician can translate some of his/her emotions musically (although, some are good in leaving out the 'e' out of emotion
) and it has an effect to a listener, I would say, that is really what it boils down to. Personally speaking, it stops right there.
As for the theory...obviously, always a touchy subject around musical circles, I don't think that it a definable attribute to be a musician. If a musician intents to work as hired musician (studio or live), then, yes, it is probably a good idea to have a solid theoretical foundation. However, if a solo artist who is a good performer and songwriter (and, perhaps, has a good record contract to top it
) doesn't know too much about circular fifth, chord substitution. etc., I don't think it's really necessary.
I believe, it's really up to an individual to learn what he thinks is best for him or her.