Rff1010, regular/original Dawn Dish detergent is another frequent recommendation from me! Sometimes we need to use what we have at home and if the issue was running dye, it would be the first choice from me. I'm suggesting trying the baby shampoo for softener effect and for a gentle lift out of any residue... I would hesitate to use actual hair softener unless I could be sure to rinse it out very well.
For my emergency kit I do keep regular bleach, original Dawn, WD40, Duct Tape, and a few other must haves on hand.