Hair dye stains on furniture made of wood are usually unsightly and removing them from such surfaces may be one hard nut to crack. Luckily several effective cleaners can help get rid of stains for good. Some of these cleaners include vinegar, baking soda, hydrogen peroxide, dishwashing soap, rubbing alcohol, vanishing, and many others. However, the best way to get this stubborn stain is by combining baking soda with liquid dishwashing soap.