Whisk together the vinegar, ketchup, sugar, celery seeds, hot sauce and 1 1/2 teaspoons salt in a large bowl until the sugar dissolves. Whisk in the oil to make a smooth dressing.
Add the cabbage and red onions to the dressing, and toss well. Cover and let stand at room temperature for about 20 minutes to wilt the cabbage slightly. (The slaw can also be made several hours ahead and refrigerated.)
Sprinkle the slaw with the parsley; toss and serve.