There are worse insults than having “too generic” hurled in your direction.
For record company A&Rs, the formerly pony-tailed ones, this is a big weapon in their arsenal, however and after the sting of it, yes, you can see the point of the rebuke. Because they know if they are listening and assessing your records with a view to signing you up that you can play, they know your image is good but they want to understand and convince themselves that you have wider appeal. Of course “record company A&Rs” only formally exist as an exotic job title in big rock and pop record major labels or their carefully liveried boutique often recently revived vintage marque imprints. On a small jazz indie level they exist too, usually the person who runs the label and does everything bar the tap-dancing, although occasionally that too as well as the ability to do the necessary paperwork fandango, or farms it all out to a few trusted assistants.
If you are looking for someone to put your record out and are turned down because you are too generic in jazz, or any line of the arts if you make the leap, it means you are too jazz. That may sound absurd but isn't.
Overly generically-guilty is slightly different than falling down on playing a style too closely or better being a deliberate stylist. Being a stylist can be a good thing and a compliment to you yet it can also be like becoming a character actor and then typecast. If this is looking like it is an issue and bothers you then you need to move on from being a stylist and that usually comes in jazz after many, many years when you turn a corner artistically, shed some of your ego, learn how to live somehow like a grown-up person, lose a few bad habits, and suddenly shed your undying reverence for the original style that you have long since cherished and tried foolishly to emulate in all obsession.
With generic there is a lot of baggage. And the problem is when you exhibit the effects of this virus then no one outside your small world can really get what you are about and can only see the style trappings that restricts their perception of you as an artist. It is not quite, or at all, as traumatic as belonging to a cult. Give it time.
You may contend that an acquisition of all-pervasive genre style attributes is the case in all jazz and is inevitable and all clinging but that is not strictly right and fatalistic. It also makes genre seem more fixed than it is and there is fluidity there beyond the orthodox notions of sub-genre identification. A good example of someone who stopped being generic or maybe never ever was is Norah Jones (as likely to dabble in country or retro Babyboomer Americana as her recent return to heartland jazz) or any other artist who has crossed over... Jamie Cullum, Melody Gardot, Lizz Wright... and they are not just singers and not just pop-jazz artists but rather anyone who can connect beyond a jazz public but still retain some of the trappings of the style even when they have made all these concessions to an outside world. John Coltrane can and did connect beyond jazz and never made any concessions artistically I ought to hastily and properly point out. And neither did Ornette Coleman who means as much to avant rock and art rock fans as he does to jazz fans. Note the present tense.
How do you become non-generic? Ah, difficult. Short answer: know the rules and break them all. Think like a listener, be an artist and not only a performer, and not only love the idea of being a jazz musician who loves to play jazz but communicate that love that bit better, no need to explain, no need to apologise, to everyone.