It depends on your definition of 'healthy' I suppose- low salt, low sugar, low carb, low fat, plant based? Almost any table service restaurant in WDW can make accomodations to the menu- grilling meat, leaving off sauces, reducing salt, etc. and most have low sugar dessert alternatives.
If you are looking for sushi, poke and dashi bowls try Kona Cafe, Morimoto's, Katsura Grill or Tokyo Dining (currently closed).
As far as counter service, Pecos Bill's and Satuli Canteen were already mentioned but Harambe Market also has rice bowls and salads and Sunshine Seasons often has several healthier choices. Tangierine Terrace is closed but hopefully when they reopen they keep their menu the same as it also has several healthier options.