Tangs such as kole eyes, and foxfaces often much on hair algae as if it were an all you can eat salad buffet. Emerald crabs are decent hair algae consumers, but they can be a bit risky around other fish if they run out.
Bryopsis, which kinda resembles hair, won't be eaten by much, however like all the other algaes, it can be starved out of nutrients. (Phosphate, silicate, nitrates.)
Your best bet is to keep up with water changes, and let the tank stablize a bit more with it's nitrates, eventually reducing the needed amount of food for the algae growth. I eventually resorted to a toothbrush and a massive water change with the addition of a skimmer and better carbon to finally beat bryopsis.