While Disney restaurants are normally willing to accomodate dietary needs....I'd think that this one might be one that they won't be able to do for you. Soup of course would have to be cooked a few hours ahead (and if that cheddar soup is actually some weird instant, please don't tell me, I do NOT want to know). And since the bacon is a part of the soup, not just a condiment sprinkled on top of it....well, that would mean that they'd have to make a batch just for you.
Now, that said, it couldn't hurt to ask, maybe the get enough requests for veggie that they make a batch to have on hand or something.
But just be prepared to be disappointed.