IMO, the ability to read either standard notation or tablature has nothing to do with "theory." Neither does where to put your fingers.
Neither does playing by ear or not. Neither does getting paid or not. (Paid for playing? What a concept!) Neither does whether you play the banjo, the calliope or the tuba.

Theory comes in when you have gotten a song down cold in C and the lead singer says "That's too low, can you do it in E-flat." If you are theoryless, you either change harmonicas, capo up, or go home.

I do not subscribe to the "Real men don't capo" idea, because there is a difference between how Wabash Cannonball sounds in C at one and how it sounds played in G capoed up to C. But that's a separate issue; I just don't want anybody objecting "well, you can always capo." You can, but sometimes for better and sometimes for worse.

Theory is knowing how to make a major into a minor, or where to add a seventh, ninth, etc. I don't know how many times people have said something like, "Where on the web can I find chord forms for a [insert instrument name] in the alternate tuning of [insert any key]?" A wee bit of theory would solve all that.

Khandu is right, for my money; a kazoo player could benefit from theory. As to knowledge blocking creativity, I strongly disagree to the point of getting nasty and saying that's an excuse for laziness.

Richie--I only half agree. Rolls are important, but what is the left hand doing in the meantime??? You can't just play "the banjo." You have to play A SONG on a banjo. And that takes theory to do well.

CC