There's a pretty significant overlap between jazz and the blues, there are a lot of jazz standards that follow a blues form and the vast majority of improvisatory scales are built around the pentatonic scales. That said, I could imagine how being a blues fan and hearing a jazz rendition would be like going to a Panera Bread and hearing that god-awful dogshit Bon-Iver-ass vocoded cover of Put Your Records On that shits all over a good song by turning it into a wankfest, I could see that being grounds for violence. Meanwhile the alligators went to Berklee and think they know everything about everything when really they just speedrun through all the fun parts of music/musicianship and have nothing left but academic exercises, but they can't bring themselves to admit that because it means accepting that they spent thousands of dollars and years of their life on a mistake. I think probably both sides need to reach an understanding of that fact without explicitly saying it; the alligators need to get over their imposter syndrome and find reverence for music as a form of expression and commiseration rather than a contest, and the crocodiles need to give a little grace to the lizards that got conned by the academic industrial complex into a decision they can't afford to regret.
I don't think they'll ever truly understand each other but they can coexist.
