We don’t truly know if dairy contributes to inflammation of scarring alopecia. There have been no studies done to prove or disapprove this.
There are patients who will say that removing dairy and gluten from their diet has helped them to ease the symptoms of lichen pilanopilaris (a type of scarring alopecia) and that their hair got better.
Therefore, there is no opposition to avoid dairy products if a patient feels that it helps them but one has to be careful to suggest that is the answer.
A good balanced diet rich in fruits is important for healthy scalp and hair. A healthy gut biome is also very important and diet rich in prebiotics and probiotics is essential. The more varied ones gut biome, the more benefits to ones health.