Actually, many restaurants across WDW have really been upping their game with vegan selections. Unfortunately, it is usually just one or 2 items per restaurant, so not a lot of variety, but there are options.
Some I can think of right off my head:
Casey’s has a vegan hot dog
Liberty Tree Tavern has a vegan meatloaf
Sunshine Seasons has several vegan options
Sci Fi Dine in has vegan lettuce wraps
Be our Guest lunch and dinner has vegan options
At Yak and Yeti, tofu can be subbed for meat
Plaza ice cream parlor offers plant based ice cream options (I can’t remember which ones exactly)
There are a lot of restaurants that offer vegan burgers and I believe at several pizza places, vegan cheese is an option (I think you have to ask for it).
I would probably just check out menus from the Disney site and go from there.
ETA...Dole Whip is vegan!!!!