Actually,I think it is a case of relative worth in certain circumstances.If it was my sweetheart who had the allergy,I can't see *not* giving up my pet.And no,I wouldn't expect her to take pills or get shots because there's not a pill or shot in existence that doesn't carry at least *some* risk.
Human beings always have been,and always will be,far more important than a pet.
It depends on whether animals are a big or small part of someone's life. Obviously, if someone's major hobby is cats, then you're asking the person to change who they are.
I'd try the desensitizing before I'd ask they change for me.