For whatever reason people might be unable, or unwilling, to eat certain things. Don't much care whether it is allergies, diet, morality, cost/geography, religion or similar for the purposes of this one. Also plays if you have friends and family that won't and you need to figure out a way to make something everybody wants.
Most times I find something being called nut, gluten, sugar, wheat*... free it is synonymous with taste free or just being on the label because it just so happens to be that by dint of the normal recipe but there are exceptions. That said I usually find what people that have to handle such things manage to do tastes pretty good and thus is worth asking.
*there are a few more ancient forms of wheat that you seem to be able to buy in even the tiny supermarket (doesn't have a clothes section it is that small) a small town near here has that some people doing some of the wheat exclusion diets might still be able to have, though be sure you read and know what you are doing here.
Myself.
Tomatoes.
I hate them and they hate me. If I eat something with tomato paste, powder or sauce (surprisingly common as they are a cheap flavour enhancer and bulking agent, also common for things to switch up and add some where normally they would not or be in other brands) it squirts out of me the other end at some pace. Eating a raw tomato would make me wretch, I could conceivably have some sauce and have done in the past (made some nice dishes even) but see previous results.
This means no contemporary pizza, no lasagne, no Branston pickle, and having to be ever observant for just about everything when out shopping.
My solution.
Jars of grilled peppers. Some consider them a southern European/Mediterranean food, certainly I found them in such shops when I was in the US. Drain them, slice them fine or blend them as necessary, and they make a serviceable red sauce for whatever needs it. I have some salt with ground up seaweed in it and it brings it up a notch, and whatever else you might do to make tomato based sauces work better will likely work here too (assuming it is not "add tomato paste"). Do note however if the recipe calls for water then do less of it as these peppers seem to contain a lot.
I also had banana ketchup the other week. Was lovely.
I don't do so well with peanuts. Cashews on the other hand, and cashew butter when peanut butter is called for, works pretty well for most things. That said it is rather expensive -- made a nice satay chicken the other week which was delicious but given a small jar of cashew butter is several times what a bog standard peanut offering is... worse is most of the combination nut butters use peanut as a bulking agent.
I ran out of eggs the other week and was making a cake. Fortunately the cupboard was stocked with all sorts of oddities here and one was an egg replacement you mix up with water. Resulting cake (one called hummingbird cake) was fine but as olive oil is the fat in that one I don't know what the wider effects are. Said olive oil based cake mix (I mostly do an apple one with apple butter or a banana one, got some pumpkin in to try at some point later) also means you dodge the butter or margarine of others but if you are after airy cake** then don't -- this is stodge cake at its finest.
**I am generally of the opinion that sponge cake is cake made for people that want to be naughty and have some cake but also punish themselves in the process.
I have tried coconut sugar in place of sugar. Maybe 70% and most of the people I know that don't do sugar will do maple syrup or fructose instead so that makes that one easier. Speaking of sugar is something calls for caster sugar then I usually go for brown or even dark brown instead.
I have yet to find a good milk replacement. Oat milk might be OK for cooking (even had some nice custard made with it) but no good for anything else.
Certainly never found a good cheese replacement, though do check what you have as it might just be cow dairy that bothers you. Tried several types and vaguely edible plastic is about as far as I get there.
Goat butter does OK when cooking things. I don't do butter normally though so eh. Not a fan of ghee really but some do well here.
I did hear the vegan magnums taste good. Don't know if I believe it myself -- vegans certainly don't taste good.
Everybody I know is a fan of garlic whether they realise it or not (my dad in particular having several stories of more elderly acquaintances saying "I don't like it", to which he had to giggle inside as "the last 50 dinners you had around here all had it, and you went back for seconds" which makes me think it is more badly cooked garlic that does people in). Still asafoetida is not without its charms here.