Most airlines I have flown on in the last 10-15 years do not serve peanuts (which, as already pointed out is not a nut, but a pea).
Peanut allergy is sort of different in that it is hazardous even if you do not touch or ingest the peanuts. Just being in the vicinity can be dangerous. So anything else can be served (strawberries, shellfish, etc..) without causing allergic reactions.
The other thing is that allergies can kill if you don't get treatment at once, and since you're stuck in a metal tube...
So, Catatonic, I definitely think that airlines should accomodate people who are allergic, since it's rather easy to do so. With the exception of the peanuts ban, all you need are special meals.
There is one other case though. My wife is violently allergic to cats, as in her eyes swell up until she is blind and she coughs uncontrollably. So I think all animals need to go in the hold regardless of size, OR
there should be specified animal free flights.
In this case though, if the airline could not guarantee a peanut free environment, and said so, I don't see their argument.