Be a reputable breeder.
While it’s a shame that a wealthy, supposedly influential terrible customer has been through your establishment and while it’s also a shame how common that is, reputable trainers and customers who are actually concerned about pokémon will care a lot more about the, well, care you put into breeding. If a bad customer spreads the word that you’re a terrible breeder because you won’t fulfill a request—as if a pokémon is an object and not a living being—then while that could damage your reputation a bit, it could also serve as a testament to your concern for quality care over the mass-production of certain traits.
Moreover, reputable trainers understand that breeding for shiny pokémon is not a guaranteed thing and that requests for shiny pokémon are not easy to fill and require enough breeding to tire out the parents and produce more hatchlings than one may be able to home. It’s only a thing that may be done with two mated pokémon that are extremely fond of each other, by a breeder with enough connections to rehome hatchlings humanely. Trainers who don’t recognize this and demand shinies anyway say more about themselves than the breeder, and a breeder who obliges says more about the way they care for their pokémon than their skills.
In short, anonymous, she was a bad customer, but no matter how she spins her story, if she convinces others to avoid your services, those others are not customers you would have wanted anyway.