We don't avoid soy but here's what I've got for meals based on info from our February trip. I can't guarantee that these are all soy free but I think they are. Definitely confirm with Special Diets as things really do change all the time.
The french fries as of February now contain soy unfortunately. If you're ok with small amounts of soy then you can find these fries everywhere that serves either allergy chicken tenders or hamburgers.
I don't think the Ener-G buns have soy but confirm that with Ener-G or Special Diets.
The French Meadow brownies I believe contain traces of soy. They can be found at most CS locations. The ones that don't carry them do carry the Enjoy Life cookies (we buy them at home they're so good).
Magic Kingdom
Columbia Harbour House: allergy chicken tenders, fruit
Cosmic Ray's: rotisserie chicken, hamburger, grilled chicken burger
Lunching Pad: turkey leg
Epcot
Sunshine Seasons: rotisserie chicken, pork chop, grilled salmon, steamed broccoli, glazed carrots, vegan black bean soup (no idea if there's soy), gluten free pasta (with advanced notice), white rice, yellow rice, rice milk, Rice Dream ice cream, Enjoy Life chocolate bars, fruit
Electric Umbrella: allergy chicken tenders, hamburger, Enjoy Life chocolate bars, fruit
Liberty Inn (American pavillion): allergy chicken tenders, hamburger, Enjoy Life chocolate bars
Turkey Cart (American Adventure): turkey leg
Turkey Cart (Test Track) turkey leg
Animal Kingdom
Restaurantosaurus: allergy chicken tenders, hamburger, Enjoy Life Cookies, Enjoy Life Chocolate bars, Rice Dream Ice Cream (around the corner at Dino Bites)
Flame Tree BBQ: rotisserie chicken, Enjoy Life cookies, Enjoy Life chocolate bars, fruit
Turkey Wagon (Discovery Island): turkey leg
Trilobites (Dinoland): turkey leg
Hollywood Studios
ABC Commissary: allergy chicken tenders, hamburger, Enjoy Life cookies, Enjoy Life chocolate bar
Backlot Express: allergy chicken tenders, hamburger, Enjoy Life cookies, Enjoy Life chocolate bar
Rosie's All American Cafe (Sunset Market): allergy chicken tenders, hamburger, Enjoy Life cookies, Enjoy Life chocolate bar (there's tons of fresh fruit right nearby)
I'm sure you can guess that Sunshine Seasons is a must do stop for us at least once during each vacation. Where else can we get such variety?
We typically don't eat a lot of CS in parks. If we'll be eating in a park then I try to do TS meals so there's more options. CS at resorts is MUCH easier with plenty more options than at parks as the chefs at resorts have lots more ingredients to work with and you'll actually have a chef prepare a meal vs a manager who only knows how to do a couple specific allergy safe foods.
For snacks, the frozen pineapple and frozen strawberry bars are delicious. I don't know if the popcorn is soy free or not; I know it's gluten and milk free. It think they use coconut oil but I'm not sure if there's also soy oil. The ice cream parlours typically carry Rice Dream ice cream though, you'll get plenty of ice cream at TS meals so IMO it's not worth waiting in line for the ice cream when you can grab a frozen fruit treat at any cart. Fresh fruit is also a refreshing and cheap snack. WDW now also has their own line of Kettle chips but I don't know if they're soy free or not. The plain ones I know are gluten and milk free but for some reason I'm suspecting soy is in there; confirm with Special Diets.