Speaking as someone who's allergic to onions, I can tell you that it is easy to skip the onions if you're doing the cooking yourself. I just leave them out of a lot of recipes, sometimes substituting more of some other flavoring, sometimes not. Green peppers are a good substitue for chopped onions in some cases where texture is an issue.

The hard part about being allergic to onions is eating food that other people make. My mother thought that simply telling my father and I that there were no onions in the food she cooked would prevent us from getting sick. Then she wondered why we got sick and didn't appreciate her cooking.