Hi!
Your allergist's advice doesn't seem odd to me, but I'm curious to hear what others think too.
I did a paper on allergy inheritance in university, and it's correct that lo1 having an egg allergy does not increase the chance of lo2 also being allergic to eggs. Specific allergies are not inherited genetically, it is the tendancy towards having allergies that gets passed down. For example, if I'm allergic to cats, ds may develop an allergy to pollen. (If you want more detail let me know, but I won't bore you if you're not interested
So given that lo1 has an allergy, it is more likely that lo2 will also develop an allergy though we cannot predict to what. Does that make sense? That is likely why your allergist advised you to cut out allergenic foods (though eggs are generally allergenic too, don't know why he specifically excluded them?)
Having said all of that, a lot of allergies run in my family and dh's family, and ds has a dairy allergy, and I haven't cut anything out of my diet while bfing. My paediatrician said it wasn't necessary unless we noticed ds reacting to something.
HTH, and good luck!
Vikki