If your cat goes outside, putting her unwanted food out for the birds is a marvellous idea. She will doubtless wolf the food on the grounds that charity begins at home. It has always worked with mine.
I have become wise to the fact that kittens and young cats should be accustomed to more than one brand of cat food, preferably three or four - that way there is a slim chance that they won't become too fussy as they grow up.
However, there are limits, where you do need to be accomodating. Three different cats were unable to eat kibble from one well-known chain of supermarkets without sicking it up again - so we obviously changed brand.
One of two successive pairs of cats loves cat food that contains liver, the sibling of each cat refused point-blank to eat it.
Cats can and do have their likes and dislikes, and there is no way a cat will eat something he or she dislikes. But we can hardly complain, can we? We have our likes and dislikes too.