We don't have picky eaters in my house, and really don't get the whole picky eater thing.
Everyone in the house is allowed one food that will not be allowed on their plate. This choice is made away from the dinner table, and not at meal time. My one food that will not touch my plate is Ketchup, it has been for years, I'll buy ketchup, even keep it in the fridge, and allow it one my table, not my plate. One family's choice is no nuts (not allergic just dislikes them) another is mustard, another is oranges. It is fully possible to eat a healthy diet with out nuts, mustard, oranges or ketchup.
Your not allowed to say "I don't like that food" at the table, if you do, I will give you more of it. The child says I don't like grapes, if you say that again I will give you more grapes, to help you get used to grapes, most children will not say they don't like grapes again. They may or may not eat the grapes, but they most likely will not complain about grapes on the table.
My oldest, years ago said she would not eat pizza unless it had broccoli on it. I explained I would be happy to put broccoli on her pizza if we have broccoli in the house.
I have no problem packing more carrots in one lunch, with no oranges, and oranges and less carrots in another. One child likes more chicken on their plate than the other, this is fine as long as they both eat the vegetables.
I don't force anyone to eat any food, it might be an allergy, besides my kids have never made me eat ketchup the only food I don't like. I don't talk about how much I hate ketchup at the table, either.