Trim and peel the rutabagas, then cut lengthwise into ½-inch planks.
Stack 2 planks and cut into ½-inch sticks. Repeat with remaining rutabaga and set aside.
Whisk cornstarch and cold water in a large bowl and set aside.
Add salt, baking soda, and a separate 1 quart water to a medium pot and bring to a boil over high heat. Skim off the foam.
Add rutabaga to the pot, return to boil, and cook just until fork-tender, about 7 minutes.
Re-whisk the cornstarch mixture to combine and, using a slotted spoon, transfer the rutabaga to the bowl with cornstarch. Fold until the cornstarch thickens and clings to the rutabaga. Set aside.
Add peanut oil to a 12-inch nonstick skillet over medium-high heat and bring to 300 F.
Using tongs, add rutabaga to the oil in batches. Fry until crispy and lightly browned on each side, flipping them halfway through frying.
Transfer rutabaga fries a baking sheet lined with a wire rack and season with salt to taste. Repeat with the remaining rutabaga fries.
Meanwhile, whisk mayonnaise and sweet chili sauce in a small bowl.
Serve fries immediately with sauce, or keep warm in a 200 F oven until ready to serve.