In 5- to 6-quart saucepot, place red potatoes and enough water to cover by 1 inch. Heat to boiling over high heat. Reduce heat to low and simmer 2 minutes. Stir in sweet potatoes, heat to boiling over high heat. Reduce heat to low, cover and simmer 8 to 10 minutes or until potatoes are just fork tender.
Meanwhile, in large bowl, with wire whisk, mix vinegar, mustard, salt and pepper.
Drain potatoes well. While hot, add potatoes to dressing in bowl. Gently stir with rubber spatula until evenly coated. Let stand until cool.
In small bowl, whisk soy mayonnaise and soy milk until smooth. Add mayonnaise mixture, celery, onion, and parsley to potato mixture. Stir gently with a rubber spatula until potatoes are well coated. Serve at room temperature, or cover and refrigerate until ready to serve.