Add the green cabbage, red cabbage, carrots, red onion, and parsley to a large mixing bowl. Toss to distribute the colors evenly.
Whisk the apple cider vinegar, sugar, Dijon mustard, celery seed, salt, black pepper, and red pepper flakes in a small bowl until the sugar begins to dissolve.
Slowly stream in the olive oil while whisking until the dressing looks glossy and evenly combined.
Pour the dressing over the vegetables and toss thoroughly, lifting the cabbage from the bottom so every ribbon is lightly coated.
Cover and refrigerate for at least 30 minutes and up to overnight. Toss again, taste, and adjust the salt, sweetness, or vinegar before serving.