A good home remedy that should work to get dye stains out of white clothes naturally is to pretreat the dye stain on the clothes with a solution of 3 tablespoons of white vinegar and 2 tablespoons liquid detergent (Persil Bio Washing Powder works best) in 1 quart (1 liter) hot water.
The hotter the water the better by beware that your clothes may not take that hot of water so use the recommended water temperature for your clothes.
Rub the solution into the dye stain, then blot it dry before washing.
Let the clothes soak in the solution for up to 30 minutes before placing the clothes in the washing machine.