Hi,
I haven't seen many posts about Sea World here so I thought I'd share my recent experience.  We were at the one in Orlando two weeks ago.  My son has allergies to peanut and shellfish. 

We had lunch at the Voyager's Smokehouse, which was a cafeteria style place - the food items are cooked in large batches.  We checked with the manager first and he told us they did not use peanut or shellfish products.  He did advise us to avoid the desserts and breads.  I saw that there was carrot cake in the dessert section, which has tree nuts, right?  I was okay with that since my son passed all his tree nut challenges last year.

For dinner, we ate at Shark's Underwater Grill, which is advertised as the most allergy friendly restaurant at Sea World.  I believe it; the chef came to talk to us and was knowledgeable and accommodating.  He said they did not use any peanut in the restaurant (don't remember about tree nuts).  The only unfortunate part for us was that there were many dishes with shrimp, so while I was not concerned about cross contamination, the options were pretty limited for my son. 

For those with shellfish allergies, be aware too that at the sting ray touch pool, people can buy shrimp to feed the rays.   They do have a sign that warns of possible contact with shellfish. 

It seems to me that Sea World has improved considerably in its allergy friendliness since our previous visit 7 years ago.  I feel a bit conflicted about having killer whales in captivity but that is a different issue!