"It seems to be a basic rule that ALL requests will have NO bearing on the style of music being performed ."

Quite!

"I think it's a form of Tourette's syndrome which makes the afflicted person call out the name of the one song or tune they've heard of featuring a particular instrument you happen to have (or one slightly resembling it, banjo, ukulele, mandolin, it's all the same)"

And yes again!

Playing for a zydeco band, I find that (fortunately) the frontline combination of frottoir (metal rubboard) and cajun accordion makes it a little difficult for the uninitiated to work out what we might or might not be able to play, so inappropriate requests are few and far between. I can see what a headache it could be if you've got a banjo or fiddle!