I tried to find the answer to "How do I remove hair dye stains from carpets" for AGES, i searched and searched but couldn't find anything that I could use easily... Anyway... I decided to ask my good old Dad who said "Have you tried white spirit?"
It worked! Dilute some white spirit onto a clean cloth and rub it over the stain. Then wash with clean water again and voila!
Might be an idea to test a small hidden area first if you are unsure.. But it worked on my woollen green bathroom carpet!