The difference between classical and jazz musicians points to a deeper conversation about diversity. Classical musicians are a cog in a big musical machine, so they are almost by definition less diverse. There's no room in a classical orchestra for a pianist who can't reach the far ends of the keyboard (Michel Petrucciani), there's no room for a guitarist with two-and-a-half working fingers on his fretting hand (Django Reinhardt), there's no room for a singer with a completely unique vocal range (Jimmy Scott).
Jazz is more amicable to diversity than classical music on a fundamental level, because it's based on improvisation and unique personal expression. If you're physically unable to play the same way as everyone else, you're pretty much useless to a classical orchestra but you may well become a pioneer in jazz.
Some obstacles to diversity can't be overcome with blind auditions and quotas and sensitivity training. Some environments are lacking in diversity because they are structurally incompatible with diversity; they can't have diversity retrofitted on to them, but need to be reformed from the ground up.