One for the (not-yet-extant) "I Hate Onions" Cookbook
In a fair number of circumstances where onions are being used as "vegetable filler" and for texture (around a pot roast, in a soup, stuffed in a turkey,) celery is a really good substitute. You can also do something like celery root, but... Almost anything has more flavor than long-cooked white onions. Even celery is more assertive. Other veggie filler/texture tends to wind up being a much larger chunk of the final flavor.
Now for *red* onion substitutes, all kinds of things would be fine - celery, celeriac, fennel, radishes... Red onions have a lot of final flavor, so something with a lot of flavor makes a good substitute. It's white onions that are so mild that it's hard to find a similar mild-texture-no-flavor equivalent.
Though I should probably be trying jicama for that. It's nearly flavorless. Anybody know if it stays crunchy after cooking?