I hatehatehate people whose eating issues take over and become everyone's issue.
I confess that I have an eating issue which does dictate where I can go when a group of friends wants to get together for food. I have a severe skin allergy to coconut. As such, I cannot set foot in a Thai restaurant ever. What's more, if someone were to eat something with coconut in it and then say, hug me, I'd be a resident of hive city for the next week. My friends and family are aware of this, but occasionally forget. If everyone else wanted to go for coconut-laden-food I'd have to just decline.
On vacation I'd not feel particularly safe being left alone in a foreign city. I think I would have to insist that something that would cause a serious medical issue abroad be avoided out of respect for my safety. If my travel buddies couldn't do that little for me I don't think we'd be friends anymore after traveling.
If you were travelling in Europe, say, I'd say that was reasonable, if you made this clear in the planning stages (no-one in the group can go to a restaurant of X type, and no-one, at any point during the trip, can eat coconut). I'm assuming, however, that you wouldn't go on a group vacation to Thailand and then insist that your group couldn't eat at Thai restaurants because it wasn't safe and you didn't want to be left alone.
Actually, on a group trip, I think that not being willing to be left alone is something that should be discussed while planning. There are a lot of people, me included, who would think that splitting up occasionally to each do their own thing would be a normal part of a group trip (personally, I'm a lot happier if I get some time by myself.) If I went on a trip with a friend and found out that I was expected to do stuff with them all the time, I would find it kind of stressful. Better to discuss that before the trip.
I do know that I'm pretty far over on the adventurous/independent side of international travelling - while there are some places I wouldn't feel safe, I've travellled alone in places where I don't speak the language, and happily eat things I can't identify (I love local markets). I have actually moved to a country where I don't speak the language by myself. So I do know that if I were planning a trip with someone, or a group, it would be important to discuss how things were going to work before making the decision to go, so we'd all either be reasonably content, or decide that we weren't good travel companions.