My oldest son is turning 9 at the end of this month. He does not like to eat: sandwiches, hamburgers, broccoli, carrots, salad, potatoes (unless they are fried), anything with tomato sauce. SO when we go out to eat or eat with our extended family there is always a fight or a struggle to get something for him to eat. He will eat PRETTY much anything that is, drumroll please, beige! french fries, chicken nuggets, cheese pizza, crackers, plain noodles.
So my husband says about once a month: your a feeding therapist, fix your kid! (in jest).
Here is why I don't worry: most of the food he rejects are mostly foods that I consider in the American style of cuisine.
Here is what he does eat: Gailan (Chinese broccoli -it is greener than american), Onchoy (Water Spinach - so wikipedia tells me), pea sprouts, and most other Asian vegetable that is green. He eats most meats stir fried in soy sauce, garlic, and ginger. He does like rice (white and brown).
He also eats sausages and potato balls that are from his German side.
Overall, he does eat a variety of foods from another culture. So, what is a true picky/limited eater? Someone that would not eat anything from ANYWHERE no matter what. Most limit eaters won't even want to be in the same room as foods that they cannot eat or tolerate.
So try different foods with your child. See if they just need to tap into their cultural taste buds.