Why don’t you just say “No milk products or eggs”?
Also, now I’m curious. Do you just happen to be allergic to both milk and eggs, or are you allergic to something they both have in common?
If it’s common to have an allergy to both, that would be a good reason to call them both dairy. Although I’m not sure it’s good to use allergies as part of these definitions, since it’s dangerous to have the imprecision of common definitions when dealing with allergies. If the only sensible thing to do is say that you’re allergic to dairy and eggs, then defining dairy to include eggs just means you’ll end up being redundant.
Why don’t you just say “No milk products or eggs”?
Also, now I’m curious. Do you just happen to be allergic to both milk and eggs, or are you allergic to something they both have in common?
If it’s common to have an allergy to both, that would be a good reason to call them both dairy. Although I’m not sure it’s good to use allergies as part of these definitions, since it’s dangerous to have the imprecision of common definitions when dealing with allergies. If the only sensible thing to do is say that you’re allergic to dairy and eggs, then defining dairy to include eggs just means you’ll end up being redundant.