In a large bowl, whisk the vinegar, sugar, 1 teaspoon salt, and ⅛ teaspoon pepper until sugar is dissolved, about 30 seconds.
Gradually add the oil, whisking until combined.
Stir in the onion and set aside for 5 minutes.
Fold in the cannellini, kidney, and green beans, and the parsley.
Gently toss to coat.
Serve immediately or let marinate, covered, in the refrigerator for 1 hour or up to overnight.
Stir gently before serving.