While I can eat practically anything (except things I am allergic to), my Father has the following issues:
He won't touch luncheon meat with his bare hands, using knives and forks to pry meat out of the packaging, and acts like his fingers are going to be burned or he will die of instant poisoning if he touches it.
He is terrified of eating sausages unless cooked to a crisp, resulting from reading some horror-fiction about American meat-packing plants. The fact that he had British parents (who ate them regularly) and we are living in Canada, where meat packing has for the most part, been clean and safe is irrelevant to him.
Practically all Italian food is shunned, for bizarre reasons - he is terrified of bad breath (he will get really close to your face and start sniffing you and mocking you after you eat anything Italian or Mexican); he calls melted cheese from pizza 'elastic'; and when my mother was still alive, she was made to prepare two types of spaghetti sauce when the family had dinner - one for the rest of us, one cup for him that looked like thick tomato juice, because he had an issue with the appearance of the real sauce. He demanded to wear 'smoked glasses' whenever it was served and made a rude comment on its appearance.
He will only eat fish and chips with white vinegar, he has a hangup about malt vinegar, due to smell issues, and also in spite of my British Grandparents using malt vinegar in the cold days. Because of its appearance, tartar sauce is a no-go.
For roast or fried chicken, apart from slicing off practically all the skin and batter, he begins to surgically slice off the slightest bit of discoloured meat that few people give a second thought about, and leaves a pile of it on the side of his plate enough to feed a starving family.
When I was younger, I had to eat my grilled cheese and bacon sandwiches in secret, as he would remove any "excess" bacon because 'it might make [me] sick'. Wrong! It never did. And yes, he micro-surgically removed the fat when bacon was cooked.
Finally, don't even think about offering him BBQ sauce, basting his steak with Kitchen Bouquet or marinade. (He thinks they make the meat foreign and spicy).
There are others, but these stick out the most.