I know people who play in both the folk world and the trad jazz scene. What tends to be the case is that people use different styles and techniques for playing within a particular genre, possibly a different instrument (Guitar for folk scene, trumpet for New Orleans Marching Band).
Whilst a different musical scene might be welcomed as something different on an occasion, I thing you would get complaints if a jazz band turned up EVERY week.

I used to live in Bradford, which was a great place as you could find all sorts of music played live in pubs. Trad jazz, rock, folk (listening), folk (sessions), rhythm & blues, bhangra, you-name-it. Often you would see the same faces there, the folkies at the jazz gig, the rock band guitarist in the folk session, the bhangra singer out with the carol singers.
I don't think that keeping stuff separate is a bad thing. You can choose what to go to see.
Quack!
GtD.