I've always gigged (for about 20+ years) & it's an integral part of my living, be it out with the rock trio, the jazz band or playing in an orchestra/opera, etc.
To me a musician is anyone who wants to make music. Period. Doesn't matter if you're a pro like me or a so-called "bedroom hobbyist." The more people making music in the world, the better as far as I'm concerned.
I actually like listening to the "have-a-go" brigade at jam sessions, etc., as I can always find new ideas. I sometimes find that my classical training does limit me in some certain respects & the originality of self-taught people can be very refreshing
In short, we can always learn something new from people, whether they're good players or otherwise.