Bring a large pot of salted water to a boil. Add the elbow macaroni and cook according to package instructions until al dente. Drain and rinse under cold water to cool.
In a large mixing bowl, combine the vegan mayonnaise, apple cider vinegar, Dijon mustard, lemon juice, salt, and black pepper. Whisk until smooth and well combined.
Add the cooled macaroni to the bowl with the dressing. Stir to coat the pasta evenly.
Fold in the chopped red onion, diced celery, diced red bell pepper, shredded carrots, and chopped parsley. Mix until all the vegetables are well distributed throughout the salad.
Taste and adjust seasoning if necessary. You may want to add a bit more salt or a splash of lemon juice for extra flavor.
Cover the salad with plastic wrap or a lid and refrigerate for at least 30 minutes to allow the flavors to meld before serving.