I haven't had dairy in years. Understand that when most people thing dairy they just think of like, cheese and drinking milk. In the US dairy is in nearly everything. Pretty much every baked good, most breads, buns, many snack foods, many fast food and processed food products. Even if it seems like a food you wouldn't think would have dairy, its can be used as flavoring and such. If dairy did have an effect on hair loss I'd assume it would be because of inflamation. However avoiding dairy could reduce you're vitamin d and vitamin k, a lack of which could actually cause hair loss.
I have had zero dairy products in years and years and I'm still balding.